Frank solutions for Mathematics - Part 2 [English] Class 10 ICSE chapter 20 - Mensuration II [Latest edition]

Find the curved surface area , the total surface area and the volume of a cone if its : 

Height = 12 cm , radius = 5 cm

Find the curved surface area , the total surface area and the volume of a cone if its : 

Height = 15 cm , radius = 8 cm

Find the curved surface area , the total surface area and the volume of a cone if its : 

Height = 16 cm , diameter = 24 cm

Find the curved surface area , the total surface area and the volume of a cone if its : 

Height = 8 cm , diameter = 12 cm

A conical tent requires 264 m² of canvas. If the slant height is 12 m, find the vertical height of the cone. 

A conical tent with a capacity of 600 m³ stands on a circular base of area 160 m² Find in m² the area of the canvas. 

A hollow metallic cylindrical tube has an internal radius of 3.5 cm and height 21 cm. The thickness of the metal tube is 0.5 cm. The tube is melted and cast into a right circular cone of height 7 cm. Find the radius of the cone, correct to one decimal place. 

A canvas tent is in the shape of a cylinder surmounted by a conical roof. The common diameter of the cone and the cylinder is 14 m. The height of the cylindrical part is 8 m and the height of the conical roof is 4 m. Find the area of the canvas used to make the tent. 

A circus tent is cylindrical to a height of 5 m and conical above it. If its diameter is 42 m and slant height of the cone is 53 m, calculate the total area of the canvas required. 

Sand from a cylindrical bucket 32 cm in height and 18 cm in radius is poured onto the ground making a conical heap 24 cm high. Find the radius of the conical heap. 

Find the radius of the circular base of the cone , if its volume is 154 cm³ and the perpendicular height is 12 cm

Find the volume of the right circular cone whose height is 12 cm and slant length is 15 cm . (π = 3.14)

Find the curved surface area of a cone whose height is 8 cm and base diameter is 12 cm .

The diameter of a right circular cylinder is 12 m and the slant height is 10 m. Find its curved surface area and the total surface area . 

The heights of two cones are in the ratio 1:3 and their base radii are in the ratio 3:1. Find the ratio of their volumes. 

The base circumferences of two cones are the same. If their slant heights are in the ratio 5 : 4, find the ratio of their curved surface areas. 

Find the height of the cone whose base radius is 5 cm and volume is 75π cm³. 

The curved surface area of a right circular cone of radius 11.3 cm is 710 cm². What is the slant height of the cone ? 

Find the volume and the surface area of the spheres in the following :

Radius= 2.1 cm 

Find the volume and the surface area of the spheres in the following :

Radius = 7 cm 

Find the volume and the surface area of the spheres in the following :

Diameter= 6.3 cm 

A cylindrical beaker of 7 cm diameter is partly filled with water. Determine the number of spherical marbles of diameter 1.4 cm that are to be submerged in it to raise the water level by 5.6 cm 

A cylindrical bucket, whose base radius is 20 cm, is filled with water to a height of 25 cm. A heavy iron spherical ball of radius 10 cm is dropped to submerge completely in water in the bucket. Find the increase in the level of water. 

A hollow metallic cylindrical tube has an internal radius of 3.5 cm and height 21 cm. The thickness of the metal tube is 0.5 cm. The tube is melted and cast into a right circular cone of height 7 cm. Find the radius of the cone, correct to one decimal place. 

Find the total surface area and volume of a hemisphere whose radius is 10 cm. 

Find the cost of painting a hemispherical dome of diameter 10 m at the rate of Rs 1.40 per square metre. 

A solid sphere metal is cut through its centre into 2 equal parts. If the diameter of the sphere is 3`1/3` cm , find the total surface of each part, correct to two decimal places. 

A circular hall, surmounted by a hemispherical roof, contains 5236 m³ of air. If the internal diameter of the room is equal to the height of the highest point of the roof from the floor, find the height of the hall. 

Find the volume of the hollow sphere whose inner diameter is 8 cm and the thickness of the material of which it is made is 1 cm . 

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

A hollow metallic sphere is 2 cm thick all around and has an external diameter of 12 cm. Find the radius of the solid sphere made by recasting this hollow sphere.

Find the diameter of the sphere for the following : 

Volume = `523 17/21` cm³

Find the diameter of the sphere for the following : 

Volume = `72pi "cm"^3`

Find the diameter of the sphere for the following : 

Surface Area = 221. 76 cm² 

Find the diameter of the sphere for the following : 

Surface Area = `576pi`cm²

A buoy is made in the form of a hemisphere surmounted by a right circular cone whose circular base coincides with the plane surface of the hemisphere. The radius of the base of the cone is 3.5 m and its volume is two-third the volume of hemisphere. Calculate the height of the cone and the surface area of the buoy, correct to two decimal places. 

A solid metallic cylinder has a radius of 2 cm and is 45 cm tall. Find the number of metallic spheres of diameter 6 cm that can be made by recasting this cylinder . 

A sphere has the same curved surface area as the curved surface area of a cone of height 36 cm and base radius 15 cm . Find the radius of the sphere . 

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

Find the radius of the sphere whose surface area is equal to its volume .

Find the radius of a sphere whose surface area is equal to the area of the circle of diameter 2.8 cm 

Find the length of the wire of diameter 4 m that can be drawn from a solid sphere of radius 9 m. 

The radius of a sphere is 9 cm. It is melted and drawn into a wire of diameter 2 mm. Find the length of the wire in metre. 

A sphere and a cone have the same radii. If their volumes are also equal, prove that the height of the cone is twice its radius. 

The radius and height of a cylinder, a cone and a sphere are same. Calculate the ratio of their volumes.