RD Sharma solutions for Mathematics [English] Class 10 chapter 14 - Surface Areas and Volumes [Latest edition]

How many balls each of radius 1cm can be made from a solid sphere of lead of radius
8cm?

How many spherical bullets each of 5cm in diameter can be cast from a rectangular block of metal 11 dm x 1m x 5 dm?

A spherical ball of radius 3cm is melted and recast into three spherical balls. The radii of the two of balls are 1.5cm and 2cm . Determine the diameter of the third ball?

2.2 Cubic dm of grass is to be drawn into a cylinder wire 0.25cm in diameter. Find the length of wire?

What length of a solid cylinder 2cm in diameter must be taken to recast into a hollow
cylinder of length 16cm, external diameter 20cm and thickness 2.5mm?

A cylindrical vessel having diameter equal to its height is full of water which is poured into two identical cylindrical vessels with diameter 42cm and height 21cm which are filled completely. Find the diameter of cylindrical vessel?

50 circular plates each of diameter 14cm and thickness 0.5cm  are placed one above other to form a right circular cylinder. Find its total surface area?

25 circular plates each of radius 10.5cm  and thickness 1.6cm are placed one above the other to form a solid circular cylinder. Find the curved surface area and volume of cylinder so formed?

Find the number of metallic circular discs with 1.5 cm base diameter and of height  0.2 cm to be melted to form a right circular cylinder of height 10 cm and diameter 4.5 cm .

How many spherical lead shots each of diameter 4.2 cm can be obtained from a solid rectangular lead piece with dimension  6cm \[\times\] 42cm \[\times\] 21 cm.

How many spherical lead shots of diameter 4 cm can be made out of a solid cube of lead whose edge measures 44 cm . 

Three cubes  of a metal whose edges are in the ratios 3 : 4 : 5 are melted and converted into a single cube whose diagonal is  \[12\sqrt{3}\]. Find the edges of the three cubes.

The diameter of a metallic sphere is equal to 9cm. it is melted and drawn into a long wire of diameter 2mm having uniform cross-section. Find the length of the wire?

An iron spherical ball has been melted and recast into smaller balls of equal size. If the radius of each of the smaller balls is 1/4 of the radius of the original ball, how many such balls are made? Compare the surface area, of all the smaller balls combined together with that of the original ball.

A copper sphere of radius 3cm is melted and recast into a right circular cone of height 3cm.find radius of base of cone?

A copper rod of diameter 1cm and length 8cm is drawn into a wire of length 18m of uniform thickness. Find thickness of wire?

The diameters of internal and external surfaces of hollow spherical shell are 10cm and 6cm respectively. If it is melted and recast into a solid cylinder of length of 2`2/3`cm, find the
diameter of the cylinder.

How many coins 1.75cm  in diameter and 2mm thick must be melted to form a cuboid 11cm x 10cm x 75cm___?

The surface area of a solid metallic sphere is 616 cm². It is melted and recast into a cone of height 28 cm. Find the diameter of the base of the cone so formed (Use it =`22/7`)

A solid metallic sphere of radius 5.6 cm is melted and solid cones each of radius 2.8 cm and height 3.2 cm are made. Find the number of such cones formed. 

A solid cuboid of iron with dimensions 53 cm ⨯ 40 cm ⨯ 15 cm is melted and recast into a cylindrical pipe. The outer and inner diameters of pipe are 8 cm and 7 cm respectively. Find the length of pipe.

The diameters of the internal and external surfaces of a hollow spherical shell are 6 cm and 10 cm respectively. If it is melted and recast and recast into a solid cylinder of diameter 14 cm, find the height of the cylinder.

A hollow sphere of internal and external diameter 4cm and 8cm is melted into a cone of base diameter 8cm. Calculate height of cone?

A hollow sphere of internal and external radii 2cm and 4cm is melted into a cone of basse radius 4cm. find the height and slant height of the cone______?

A spherical ball of radius 3cm is melted and recast into three spherical balls. The radii of the two of balls are 1.5cm and 2cm . Determine the diameter of the third ball?

A path 2m wide surrounds a circular pond of diameter 40m. how many cubic meters of gravel are required to grave the path to a depth of 20cm ?

A 16m deep well with diameter 3.5m is dug up and the earth from it is spread evenly to form a platform 27.5m by 7m. Find height of platform?

A well of diameter 2m is dug14m deep. The earth taken out of it is spread evenly all around it to form an embankment of height 40cm. Find width of the embankment?

A well with inner radius 4m is dug 14m deep earth taken out of it has been spread evenly all around a width of 3m it to form an embankment. Find the height of the embankment?

A well of diameter 3 m is dug 14 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment.

Find the volume of the largest right circular cone that can be cut out of a cube where edgeis 9cm?

Rain water, which falls on a flat rectangular surface of length 6cm and breath 4m is
transferred into a cylindrical vessel of internal radius 20cm. What will be the height of
water in the cylindrical vessel if a rainfall of 1cm has fallen____?

In a rain-water harvesting system, the rain-water from a roof of 22 m × 20 m drains into a cylindrical tank having diameter of base 2 m and height 3·5 m. If the tank is full, find the rainfall in cm. Write your views on water conservation.

A conical flask is full of water. The flask has base radius r and height h. The water is poured into a cylindrical flask of base-radius mr. Find the height of water in the cylindrical flask.

A rectangular tank 15m long and 11m broad is required to receive entire liquid contents from a full cylindrical tank of internal diameter 21m and length 5m. Find least height of tank that will serve purpose .

A hemispherical bowl of internal radius 9 cm is full of liquid. The liquid is to be filled into cylindrical shaped small bottles each of diameter 3 cm and height 4 cm. How many bottles are necessary to empty the bowl?

A cylindrical tube of radius 12cm contains water to a depth of 20cm. A spherical ball is dropped into the tube and the level of the water is raised by 6.75cm.Find the radius of the ball .

500 persons have to dip in a rectangular tank which is 80m long and 50m broad. What is the rise in the level of water in the tank, if the average displacement of water by a person is 0.04m³ .

A cylindrical jar of radius 6cm contains oil. Iron sphere each of radius 1.5cm are immersed in the oil. How many spheres are necessary to raise level of the oil by two centimetress?

A cylindrical tube of radius 12cm contains water to a depth of 20cm. A spherical ball of radius 9cm is dropped into the tube and thus level of water is raised by hcm. What is the value of h.

Metal spheres each of radius 2cm are packed into a rectangular box of internal dimension 16cm x 8cm x 8cm when 16 spheres are packed the box is filled with preservative liquid. Find volume of this liquid?

A vessel in the shape of cuboid ontains some water. If these identical spheres are immersed in the water, the level of water is increased by 2cm. if the area of base of cuboid is 160cm² and its height 12cm, determine radius of any of spheres?

150 spherical marbles, each of diameter 1.4 cm, are dropped in a cylindrical vessel of diameter 7 cm containing some water, which are completely immersed in  water. Find the rise in the level of water in the vessel.

Sushant has a vessel, of the form of an inverted cone, open at the top, of height 11 cm and radius of top as 2.5 cm and is full of water. Metallic spherical balls each of diameter 0.5 cm are put in the vessel due to which 2/5 th of the water in the vessel flows out. Find how many balls were put in the vessel. Sushant made the arrangement so that the water that flows out irrigates the flower beds. What value has been shown by Sushant?

16 glass spheres each of radius  2 cm are packed into a cuboidal box of internal dimensions  \[16 cm \times 8 cm \times 8 cm\] and then the box is filled with water . Find the volume of the water filled in the box .

Water flows through a cylindrical pipe , whose inner radius is 1 cm , at the rate of 80 cm /sec in an empty cylindrical tank , the radius of whose base is 40 cm . What is the rise of water level in tank in half an hour ? 

Water in a canal 1.5m wide and 6m deep is flowering with a speed of 10km/ hr. how much area will it irrigate in 30 minutes if 8cm of standing water is desired?

A cylindrical tank full of water is emptied by a pipe at the rate of 225 litres per minute. How much time will it take to empty half the tank, if the diameter of its base is 3 m and its height is 3.5 m? [Use \[\pi = \frac{22}{7}\]]

Water is flowing at the rate of 2.52 km/h through a cylindrical pipe into a cylindrical tank, the radius of whose base is 40 cm. If the increase in the level of water in the tank, in half an hour is 3.15 m, find the internal diameter of the pipe.

Water flows at the rate of 15 km/hr through a pipe of diameter 14 cm into a cuboidal pond which is 50 m long and 44 m wide . In what time will the level of water in the pond rise by 21 cm.  

A canal is 300 cm wide and 120 cm deep. The water in the canal is flowing with a speed of 20 km/hr. How much area will it irrigate in 20 minutes if 8 cm of standing water is desired ?

The sum of the radius of base and height of a solid right circular cylinder is 37 cm. If the total surface area of the solid cylinder is 1628 sq. cm, find the volume of the cylinder. `("use " pi=22/7)`

A tent of height 77dm is in the form a right circular cylinder of diameter 36m and height 44dm surmounted by a right circular cone. Find the cost of canvas at Rs.3.50 per m² ?

The largest sphere is to be curved out of a right circular of radius 7cm and height 14cm. find volume of sphere?

A right angled triangle whose sides are 3 cm, 4 cm and 5 cm is revolved about the sides containing the right angle in two days. Find the difference in columes of the two cones so formed. Also, find their curved surfaces.

A 5 m wide cloth is used to make a conical tent of base diameter 14 m and height 24 m. Find the cost of cloth used at the rate of Rs 25 per metre ?\[[Use \pi = \frac{22}{7}]\]

The volume of a hemisphere is 2425`1/2cm^3`cm. Find its curved surface area?

The difference between outer and inner curved surface areas of a hollow right circular cylinder 14cm long is 88cm². If the volume of metal used in making cylinder is 176cm³.find the outer and inner diameters of the cylinder____?

The internal and external diameters of a hollow hemisphere vessel are 21cm and 25.2 cm The cost of painting 1cm² of the surface is 10paise. Find total cost to paint the vessel all
over______?

Prove that the surface area of a sphere is equal to the curved surface area of the circumference cylinder__?

If the total surface area of a solid hemisphere is 462 cm2 , find its volume.[Take π=22/7]

Water flows at the rate of 10 m / minute  through a cylindrical pipe 5 mm in diameter . How long would it take to fill a conical vessel whose diameter at the base is 40 cm and depth 24 cm.

A solid right circular  cone of height 120 cm and radius 60 cm is placed in a right circular cylinder full of water of height 180 cm such that it touches the bottom . Find the volume of water left in the cylinder , if the radius of the cylinder is equal to the radius of te cone 

A heap of rice in the form of a cone of diameter 9 m  and height 3.5 m. Find the volume of rice. How much canvas cloth is required to cover the heap  ?

A cylindrical bucket, 32 cm high and with radius of base 18 cm, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm. Find the radius and slant height of the heap.

A hemispherical bowl of internal radius 9 cm  is full of liquid . The liquid is to be filled into cylindrical shaped bottles each of radius 1.5 cm and height 4 cm . How many bottles  are needed to empty the bowl ?

The `3/4` th part of a conical vessel of internal radius 5 cm and height 24 cm is full of water. The water is emptied into a cylindrical vessel with internal radius 10 cm. Find the height of water in cylindrical vessel. 

A tent is in the form of a right circular cylinder surmounted by a cone. The diameter of cylinder is 24 m. The height of the cylindrical portion is 11 m while the vertex of the cone is 16 m above the ground. Find the area of canvas required for the tent.

A rocket is in the form of a circular cylinder closed at the lower end with a cone of the same radius attached to the top. The cylinder is of radius 2.5m and height 21m and the cone has a slant height 8m. Calculate total surface area and volume of the rocket?

A tent of height 77dm is in the form a right circular cylinder of diameter 36m and height 44dm surmounted by a right circular cone. Find the cost of canvas at Rs.3.50 per m² ?

A toy is in the form of a cone surmounted on a hemisphere. The diameter of the base and the height of cone are 6cm and 4cm. determine surface area of toy?

A solid is in the form of a right circular cylinder, with a hemisphere at one end and a cone at the other end. The radius of the common base is 3.5 cm and the heights of the cylindrical and conical portions are 10 cm. and 6 cm, respectively. Find the total surface area of the solid. (Use π =`22/7`)

A toy is in the shape of a right circular cylinder with a hemisphere on one end and a cone on the other. The radius and height of the cylindrical part are 5 cm and 13 cm respectively.The radii of the hemispherical and conical parts are the same as that of the cylindrical part.Find the surface area of the toy if the total height of the toy is 30 cm.

A cylindrical tub of radius 5 cm and length 9.8 cm is full of water. A solid in the form of a right circular cone mounted on a hemisphere is immersed in the tub. If the radius of the hemisphere is immersed in the tub. If the radius of the hemi-sphere is 3.5 cm and height of the cone outside the hemisphere is 5 cm, find the volume of the water left in the tub (Take π = 22/7)

A circus tent has cylindrical shape surmounted by a conical roof. The radius of the cylindrical base is 20 m. The heights of the cylindrical and conical portions are 4.2 m and 2.1 m respectively. Find the volume of the tent.

A petrol tank is a cylinder of base diameter 21 cm and length 18 cm fitted with conical ends each of axis length 9 cm. Determine the capacity of the tank.

A conical hole is drilled in a circular cylinder of height 12 cm and base radius 5 cm. The height and the base radius of the cone are also the same. Find the whole surface and volume of the remaining cylinder.

A tent is in the form of a cylinder of diameter 20 m and height 2.5 m, surmounted by a cone of equal base and height 7.5 m. Find the capacity of the tent and the cost of the canvas at Rs 100 per square metre.

A boiler is in the form of a cylinder 2 m long with hemispherical ends each of 2 metre diameter. Find the volume of the boiler.

A vessel is a hollow cylinder fitted with a hemispherical bottom of the same base. The depth of the cylinder is `14/3`  m and the diameter of hemisphere is 3.5 m. Calculate the volume and the internal surface area of the solid.

A solid is composed of a cylinder with hemispherical ends. If the whole length of the solid is 104 cm and the radius of each of the hemispherical ends is 7 cm, find the cost of polishing its surface at the rate of Rs 10 per dm² .

A cylindrical vessel of diameter 14cm and height 42cm is fixed symmetrically inside a similar vessel of diameter 16cm and height 42 . cm The total space between two vessels is filled with cork dust for heat insulation purpose. How many cubic cms of cork dust will be
required?

A cylindrical road roller made of iron is 1 m long, Its internal diameter is 54 cm and the thickness of the iron sheet used in making the roller is 9 cm. Find the mass of the roller, if 1 cm³ of iron has 7.8 gm mass. (Use π = 3.14)

A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel. [Use `pi = 22/7`]

A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy [Use π =`22/7`]

The difference between outside and inside surface areas of cylindrical metallic pipe 14 cm long is 44 m². If the pipe is made of 99 cm³ of metal, find the outer and inner radii of the pipe.

A right circular cylinder having diameter 12 cm and height 15 cm is full ice-cream. The ice-cream is to be filled in cones of height 12 cm and diameter 6 cm having a hemispherical shape on the top. Find the number of such cones which can be filled with ice-cream.

A solid iron pole having cylindrical portion 110 cm high and of base diameter 12 cm is surmounted by a cone 9 cm high. Find the mass of the pole, given that the mass of 1 cm³of iron is 8 gm.

A solid toy is in the form of a hemisphere surmounted by a right circular cone. height of the cone is 2 cm and the diameter of the base is 4 cm. If a right circular cylinder circumscribes the toy, find  how much more space it will cover.

A solid consisting of a right circular cone of height 120 cm and radius 60 cm standing on a hemisphere of radius 60 cm is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is 60 cm and its height is 180 cm. Use [π = `22/7`]

A cylindrical vessel with internal diameter 10 cm and height 10.5 cm is full of water. A solid cone of base diameter 7 cm and height 6 cm is completely immersed in water. Find the value of water (i) displaced out of the cylinder (ii) left in the cylinder. (Take π 22/7)

A hemispherical depression is cut out from one face of a cubical wooden block of edge 21 cm, such that the diameter of the hemisphere is equal to the edge of the cube. Determine the volume and total surface area of the remaining block.

A toy is in the form of a hemisphere surmounted by a right circular cone of the same base radius as that of the hemisphere. If the radius of the base of the cone is 21 cm and its volume is `2/3` of the volume of hemisphere, calculate the height of the cone and the surface area of the toy.
 `(use pi = 22/7)`

A solid is in the shape of a cone surmounted on a hemisphere, the radius of each of them is being 3.5 cm and the total height of solid is 9.5 cm. Find the volume of the solid. (Use π = 22/7).

A wooden toy was made by scooping out a hemisphere of same radius from each end of a solid cylinder. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm, find the volume of wood in the toy. `[\text{Use}pi 22/7]`

The largest possible sphere is carved out of a wooden solid cube of side 7 em. Find the volume of the wood left. (Use\[\pi = \frac{22}{7}\]).

From a solid cylinder of height 2.8 cm and diameter 4.2 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid [take π=22/7]

The largest cone is curved out from one face of solid cube of side 21 cm. Find the volume of the remaining solid. 

A solid wooden toy is in the form of a hemisphere surrounded by a cone of same radius. The radius of hemisphere is 3.5 cm and the total wood used in the making of toy is 166 `5/6`  cm³. Find the height of the toy. Also, find the cost of painting the hemispherical part of the toy at the rate of Rs 10 per cm^{2 .}[Use`pi=22/7`]

In Fig. 5, from a cuboidal solid metallic block, of dimensions 15cm ✕ 10cm ✕ 5cm, a cylindrical hole of diameter 7 cm is drilled out. Find the surface area of the remaining block [Use

`pi=22/7`]

 A building is in the form of a cylinder surmounted by a hemi-spherical vaulted dome and contains  \[41\frac{19}{21} m^3\] of air. If the internal diameter of dome is equal to its total height  above the floor , find the height of the building ?

A pen stand made of wood is in the shape of a cuboid with four conical depression and a cubical depression to hold the pens and pins , respectively . The dimension of the cuboid are  \[10 cm \times 5 cm \times 4 cm\].

The radius of each of the conical depression is 0.5 cm and the depth is 2.1 cm . The edge of the cubical depression is 3 cm . Find the volume of the wood in the entire stand. 

A building is in the form of a cylinder surrounded by a hemispherical dome. The base diameter of the dome is equal to  \[\frac{2}{3}\] of the total height of the building . Find the height of the building , if it contains  \[67\frac{1}{21} m^3\].

A solid toy s in the form of a hemisphere  surrounded by a right circular cone . The height of cone is 4 cm and the diameter of the base is 8 cm . Determine the volume of the toy. If a cube circumscribes the toy , then find the difference of the volumes of cube and the toy .

A circus tent is in the shape of cylinder surmounted by a conical top of same diameter. If their common diameter is 56 m, the height of the cylindrical part is 6 m and the total height of the tent above the ground is 27 m, find the area of the canvas used in making the tent.

A bucket has top and bottom diameter of 40 cm and 20 cm respectively. Find the volume of the bucket if its depth is 12 cm. Also, find the cost of tin sheet used for making the bucket at the rate of Rs. 1.20 per dm² . (Use π = 3.14)

A frustum of a right circular cone has a diameter of base 20 cm, of top 12 cm, and height 3 cm. Find the area of its whole surface and volume.

The slant height of a frustum of a cone is 4 cm and the perimeters (circumference) of its circular ends are 18 cm and 6 cm. find the curved surface area of the frustum.

The perimeters of the ends of a frustum of a right circular cone are 44 cm and 33 cm. If the height of the frustum be 16 cm, find its volume, the slant surface and the total surface.

If the radii of the circular ends of a conical bucket which is 45 cm high be 28 cm and 7 cm, find the capacity of the bucket. (Use π = 22/7).

The height of a cone is 20 cm. A small cone is cut off from the top by a plane parallel to the base. If its volume be 1/125 of the volume of the original cone, determine at what height above the base the section is made.

If the radii of circular ends of a bucket 24cm high are 5cm and 15cm. find surface area of
bucket?

The radii of the circular bases of a frustum of a right circular cone are 12 cm and 3 cm and the height is 12 cm. Find the total surface area and the volume of the frustum.

A tent consists of a frustum of a cone capped by a cone. If the radii of the ends of the frustum be 13 m and 7 m , the height of the frustum be 8 m and the slant height of the conical cap be 12 m, find the canvas required for the tent. (Take : π = 22/7)

A milk container of height 16 cm is made of metal sheet in the form of a frustum of a cone with radii of its lower and upper ends as 8 cm and 20 cm respectively . Find the cost of milk at the rate of ₹44 per litre which the container can hold. 

A bucket is in the form of a frustum of a cone of height 30 cm with radii of its lower and upper ends as 10 cm and 20 cm respectively. Find the capacity and surface area of the  bucket. Also, find the cost of milk which can completely fill the container , at thr rate of ₹25 per litre. (Use \[\pi = 3 . 14) .\]

A bucket is in the form of a frustum of a cone with a capacity of 12308.8 cm³ of water.The radii of the top and bottom circular ends are 20 cm and 12 cm respectively. Find the height of the bucket and the area of the metal sheet used in its making. (Use 𝜋 = 3.14).

A bucket made of aluminum sheet is of height 20cm and its upper and lower ends are of radius 25cm an 10cm, find cost of making bucket if the aluminum sheet costs Rs 70 per
100 cm²

A bucket made up of a metal sheet is in form of a frustum of cone of height 16cm with diameters of its lower and upper ends as 16cm and 40cm. find the volume of bucket. Also find cost of bucket if the cost of metal sheet used is Rs 20 per 100 cm²

A solid is in the shape of a frustum of a cone. The diameter of two circular ends are 60cm and 36cm and height is 9cm. find area of its whole surface and volume?

A milk container is made of metal sheet in the shape of frustum of a cone whose volume is 10459 `3/7` cm³. The radii of its lower and upper circular ends are 8cm and 20cm. find the cost of metal sheet used in making container at rate of  Rs 1.4  per cm²?

A solid cone of base radius 10 cm is cut into two part through the mid-point of its height, by a plane parallel to its base. Find the ratio in the volumes of two parts of the cone.

A bucket open at the top, and made up of a metal sheet is in the form of a frustum of a cone. The depth of the bucket is 24 cm and the diameters of its upper and lower circular ends are 30 cm and 10 cm respectively. Find the cost of metal sheet used in it at the rate of Rs 10 per 100 cm². [Use π = 3.14] 

In Fig. 4, from the top of a solid cone of height 12 cm and base radius 6 cm, a cone of height 4 cm is removed by a plane parallel to the base. Find the total surface area of the remaining solid. (Use `pi=22/7` and `sqrt5=2.236`)

The height of a cone is 10 cm. The cone is divided into two parts using a plane parallel to its base at the middle of its height. Find the ratio of the volumes of the two parts.

A reservoir in the form of the frustum of a right circular cone contains 44 × 10⁷ litres of water which fills it completely. The radii of the bottom and top of the reservoir are 50 metres and 100 metres respectively. Find the depth of water and the lateral surface area of the reservoir. (Take: π = 22/7)

A metallic sphere 1 dm in diameter is beaten into a circular sheet of uniform thickness equal to 1 mm. Find the radius of the sheet.

Three solid spheres of radii 3, 4 and 5 cm respectively are melted and converted into a single solid sphere. Find the radius of this sphere.

A well with 10 m inside diameter is dug 8.4 m deep. Earth taken out of it is spread all around it to a width of 7.5 m to form an embankment. Find the height of the embankment.

In the middle of a rectangular field measuring 30 m × 20 m, a well of 7 m diameter and 10 m depth is dug. The earth so removed is evenly spread over the remaining part of the field. Find the height through which the level of the field is raised.

The inner and outer radii of a hollow cylinder are 15 cm and 20 cm, respectively. The cylinder is melted and recast into a solid cylinder of the same height. Find the radius of the base of new cylinder.

A cylindrical bucket 28 cm in diameter and 72 cm high is full of water. The water is emptied into a rectangular tank 66 cm long and 28 cm wide. Find the height of the water level in the tank.

A well of diameter 3 m is dug 14 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment.

A sphere of diameter 5 cm is dropped into a cylindrical vessel partly filled with water. The diameter of the base of the vessel is 10 cm. If the sphere is completely submerged, by how much will the level of water rise?

A spherical ball of iron has been melted and made into smaller balls. If the radius of each smaller ball is one-fourth of the radius of the original one, how many such balls can be made?

Find the depth of a cylindrical tank of radius 28 m, if its capacity is equal to that of a rectangular tank of size 28 m × 16 m × 11 m.

A hemispherical bowl of internal radius 15 cm contains a liquid. The liquid is to be filled into cylindrical-shaped bottles of diameter 5 cm and height 6 cm. How many bottles are necessary to empty the bowl?

In a cylindrical vessel of diameter 24 cm, filled up with sufficient quantity of water, a solid spherical ball of radius 6 cm is completely immersed. Find the increase in height of water level.

A solid metallic sphere of diameter 28 cm is melted and recast into a number of smaller cones, each of diameter  4 \[\frac{2}{3}\] cm and height 3 cm. Find the number of cones so formed.

The diameter of a copper sphere is 18 cm. The sphere is melted and is drawn into a long wire of uniform circular cross-section. If the length of the wire is 108 m, find its diameter.

A metallic sphere of radius 10.5 cm is melted and thus recast into small cones, each of radius 3.5 cm and height 3 cm. Find how many cones are obtained.

The height of a solid cylinder is 15 cm and the diameter of its base is 7 cm. Two equal conical holes each of radius 3 cm and height 4 cm are cut off. Find the volume of the remaining solid.

A solid is composed of a cylinder with hemispherical ends. If the length of the whole solid is 108 cm and the diameter of the cylinder is 36 cm, find the cost of polishing the surface at the rate of 7 paise per cm² .

The surface area of a sphere is the same as the curved surface area of a cone having the radius of the base as 120 cm and height 160 cm. Find the radius of the sphere.

If r₁ and r₂ be the radii of two solid metallic spheres and if they are melted into one solid sphere, prove that the radius of the new sphere is \[\left( r_1^3 + r_2^3 \right)^\frac{1}{3}\].

A hemispherical tank full of water is emptied by a pipe at the rate of \[\frac{25}{7}\] litres per second. How much time will it take to half-empty the tank, If the tank is 3 metres in diameter?

The radius of the base of a right circular cone of semi-vertical angle α is r. Show that its volume is \[\frac{1}{3} \pi r^3\] cot α and curved surface area is πr² cosec α.

An iron pillar consists of a cylindrical portion 2.8 m high and 20 cm in diameter and a cone 42 cm high is surmounting it. Find the weight of the pillar, given that 1 cubic cm of iron weighs 7.5 gm.

The height of a solid cylinder is 15 cm and the diameter of its base is 7 cm. Two equal conical holes each of radius 3 cm and height 4 cm are cut off. Find the volume of the remaining solid.

A solid is composed of a cylinder with hemispherical ends. If the length of the whole solid is 108 cm and the diameter of the cylinder is 36 cm, find the cost of polishing the surface at the rate of 7 paise per cm² .

The largest sphere is to be curved out of a right circular of radius 7cm and height 14cm. find volume of sphere?

A tent is in the form of a right circular cylinder surmounted by a cone. The diameter of cylinder is 24 m. The height of the cylindrical portion is 11 m while the vertex of the cone is 16 m above the ground. Find the area of canvas required for the tent.

A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy [Use π =`22/7`]

An iron pole consisting  of a cylindrical portion 110 cm high and of base diameter 12 cm is surmounted by a cone 9 cm high. Find the mass of the pole, given that 1 cm³ of iron has 8 gram mass approximately. (Use : π = 355/115)

A right angled triangle with sides 3 cm and 4 cm is revolved around its hypotenuse. Find the volume of the double cone thus generated.

A toy is in the form of a cone surmounted on a hemisphere. The diameter of the base and the height of cone are 6cm and 4cm. determine surface area of toy?

A golf ball has diameter equal to 4.2 cm. Its surface has 200 dimples each of radius 2 mm. Calculate the total surface area which is exposed to the surroundings assuming that the dimples are hemispherical.

A frustum of a cone is 9 cm thick and the diameters of its circular ends are 28 cm and 4 cm. Find the volume and lateral surface area of the frustum.
(Take π = 22/7).

An oil funnel of tin sheet consists of a cylindrical portion 10 cm long attached to a frustum of a cone. If the total height be 22 cm, the diameter of the cylindrical portion 8 cm and the diameter of the top of the funnel 18 cm, find the area of the tin required.(Use π = 22/7).

A container open at the top, is in the form of a frustum of a cone of height 24 cm with radii of its lower and upper circular ends, as 8 cm and 20 cm respectively. Find the cost of milk which can completely fill the container. at the rate of 21 per litre. [use π=22/7]

A wall 24 m , 0.4 m thick and 6 m high is constructed with the bricks each of dimensions 25 cm  \[\times\] 16 cm \[\times\] 10 cm . If the mortar occupies  \[\frac{1}{10}th\] of the volume of the wall, then find the number of bricks used in constructing the wall.

Two solid cones A and B are placed in a cylindrical tube as shown in fig .16.76. The ratio of their capacities are 2: 1 . Find the heights and capacities of the cones . Also, find the volume of the remaining portion of the cylinder.

An icecream cone full of icecream having radius 5 cm and height 10 cm as shown in fig. 16.77. Calculate the volume of icecream , provided that its 1/ 6 part is left unfilled with icecream .

A metallic hemisphere is melted and recast in the shape of a cone with the same base radius R as that of the hemisphere. If H is the height of the cone, then write the values of \[\frac{H}{R} .\]

A right circular cone and a right circular cylinder have equal base and equal height. If the radius of the base and height are in the ratio 5 : 12, write the ratio of the total surface area of the cylinder to that of the cone.

A cylinder, a cone and a hemisphere are of equal base and have the same height. What is the ratio of their volumes?

The radii of two cones are in the ratio 2 : 1 and their volumes are equal. What is the ratio of their heights?

Two cones have their heights in the ratio 1 : 3 and radii 3 : 1. What is the ratio of their volumes?

A hemisphere and a cone have equal bases. If their heights are also equal, then what is the ratio of their curved surfaces?

If r₁ and r₂ denote the radii of the circular bases of the frustum of a cone such that r₁ > r₂, then write the ratio of the height of the cone of which the frustum is a part to the height fo the frustum.

If the areas of circular bases of a frustum of a cone are 4 cm² and 9 cm² respectively and the height of the frustum is 12 cm. What is the volume of the frustum?

The diameter of a sphere is 6 cm. It is melted and drawn in to a wire of diameter 2 mm. The length of the wire is

A metallic sphere of radius 10.5 cm is melted and then recast into small cones, each of radius 3.5 cm and height 3 cm. The number of such cones is

A solid is hemispherical at the bottom and conical above. If the surface areas of the two parts are equal, then the ratio of its radius and the height of its conical part is

A solid sphere of radius r is melted and cast into the shape of a solid cone of height r, the radius of the base of the cone is

The material of a cone is converted into the shape of a cylinder of equal radius. If height of the cylinder is 5 cm, then height of the cone is

A circus tent is cylindrical to a height of 4 m and conical above it. If its diameter is 105 m and its slant height is 40 m, the total area of the canvas required in m² is

The number of solid spheres, each of diameter 6 cm that can be made by melting a solid metal cylinder of height 45 cm and diameter 4 cm, is:

A sphere of radius 6 cm is dropped into a cylindrical vessel partly filled with water. The radius of the vessel is 8 cm. If the sphere is submerged completely, then the surface of the water rises by

If the radii of the circular ends of a bucket of height 40 cm are of lengths 35 cm and 14 cm, then the volume of the bucket in cubic centimeters, is

If a cone is cut into two parts by a horizontal plane passing through the mid-point of its axis, the ratio of the volumes of the upper part and the cone is

The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to the base. If its volume be \[\frac{1}{27}\] of the volume of the given cone, then the height above the base at which the section has been made, is

A solid consists of a circular cylinder with an exact fitting right circular cone placed at the top. The height of the cone is h. If the total volume of the solid is 3 times the volume of the cone, then the height of the circular is

A reservoir is in the shape of a frustum of a right circular cone. It is 8 m across at the top and 4 m across at the bottom. If it is 6 m deep, then its capacity is

Water flows at the rate of 10 metre per minute from a cylindrical pipe 5 mm in diameter. How long will it take to fill up a conical vessel whose diameter at the base is 40 cm and depth 24 cm?

A cylindrical vessel 32 cm high and 18 cm as the radius of the base, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, the radius of its base is

The curved surface area of a right circular cone of height 15 cm and base diameter 16 cm is

A right triangle with sides 3 cm, 4 cm and 5 cm is rotated about the side of 3 cm to form a cone. The volume of the cone so formed is

The curved surface area of a cylinder is 264 m² and its volume is 924 m³. The ratio of its diameter to its height is

A cylinder with base radius of 8 cm and height of 2 cm is melted to form a cone of height 6 cm. The radius of the cone is

The volumes of two spheres are in the ratio 64 : 27. The ratio of their surface areas is

If three metallic spheres of radii 6 cm, 8 cm and 10 cm are melted to form a single sphere, the diameter of the sphere is

The surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 12 cm each. The radius of the sphere is

The volume of the greatest sphere that can be cut off from a cylindrical log of wood of base radius 1 cm and height 5 cm is

A cylindrical vessel of radius 4 cm contains water. A solid sphere of radius 3 cm is lowered into the water until it is completely immersed. The water level in the vessel will rise by

12 spheres of the same size are made from melting a solid cylinder of 16 cm diameter and 2 cm height. The diameter of each sphere is

A solid metallic spherical ball of diameter 6 cm is melted and recast into a cone with diameter of the base as 12 cm. The height of the cone is

A hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted into a cone of base diameter 8 cm. The height of the cone is

A solid piece of iron of dimensions 49 × 33 × 24 cm is moulded into a sphere. The radius of the sphere is

The ratio of lateral surface area to the total surface area of a cylinder with base diameter 1.6 m and height 20 cm is

A solid consists of a circular cylinder surmounted by a right circular cone. The height of the cone is h. If the total height of the solid is 3 times the volume of the cone, then the height of the cylinder is

The maximum volume of a cone that can be carved out of a solid hemisphere of radius r is

The radii of two cylinders are in the ratio 3 : 5. If their heights are in the ratio 2 : 3, then the ratio of their curved surface areas is

A right circular cylinder of radius r and height h (h = 2r) just encloses a sphere of diameter

The radii of the circular ends of a frustum are 6 cm and 14 cm. If its slant height is 10 cm, then its vertical height is

The height and radius of the cone of which the frustum is a part are h₁ and r₁ respectively. If h₂ and r₂ are the heights and radius of the smaller base of the frustum respectively and h₂ : h₁ = 1 : 2, then r₂ : r₁ is equal to

The diameters of the ends of a frustum of a cone are 32 cm and 20 cm. If its slant height is 10 cm, then its lateral surface area is

A solid frustum is of height 8 cm. If the radii of its lower and upper ends are 3 cm and 9 cm respectively, then its slant height is

The radii of the ends of a bucket 16 cm height are 20 cm and 8 cm. The curved surface area of the bucket is

The diameters of the top and the bottom portions of a bucket are 42 cm and 28 cm respectively. If the height of the bucket is 24 cm, then the cost of painting its outer surface at the rate of 50 paise / cm² is

If four times the sum of the areas of two circular faces of a cylinder of height 8 cm is equal to twice the curve surface area, then diameter of the cylinder is

If the radius of the base of a right circular cylinder is halved, keeping the height the same, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is:

A metalic solid cone is melted to form a solid cylinder of equal radius. If the height of the cylinder is 6 cm, then the height of the cone was

A rectangular sheet of paper 40 cm × 22 cm, is rolled to form a hollow cylinder of height 40 cm. The radius of the cylinder (in cm) is ______.

The number of solid spheres, each of diameter 6 cm that can be made by melting a solid metal cylinder of height 45 cm and diameter 4 cm, is:

The volumes of two spheres are in the ratio 64 : 27. The ratio of their surface areas is

A right circular cylinder of radius r and height h (h = 2r) just encloses a sphere of diameter

In a right circular cone , the cross-section made by a plane parallel to the base is a 

If two solid-hemisphere s of same base radius r are joined together along their bases , then curved surface area  of this new solid is 

The diameters of two circular ends of the bucket are 44 cm and 24 cm . The height of the bucket is 35 cm . The capacity of the bucket is

No Question.