NCERT solutions for Mathematics [English] Class 9 chapter 11 - Surface Area and Volumes [Latest edition]

Diameter of the base of a cone is 10.5 cm and its slant height is 10 cm. Find its curved surface area.

`["Assume "pi=22/7]`

Find the total surface area of a cone, if its slant height is 21 m and diameter of its base is 24 m.

`["Assume "pi=22/7]`

Curved surface area of a cone is 308 cm² and its slant height is 14 cm. Find

1. radius of the base and
2. total surface area of the cone.

`["Assume "pi =22/7]`

A conical tent is 10 m high and the radius of its base is 24 m. Find

1. slant height of the tent.
2. cost of the canvas required to make the tent, if the cost of 1 m² canvas is ₹ 70.

`["Assume "pi=22/7]`

What length of tarpaulin 3 m wide will be required to make conical tent of height 8 m and base radius 6 m? Assume that the extra length of material that will be required for stitching margins and wastage in cutting is approximately 20 cm. [Use π = 3.14]

The slant height and base diameter of a conical tomb are 25 m and 14 m respectively. Find the cost of white-washing its curved surface at the rate of ₹ 210 per 100 m².

`["Assume "pi=22/7]`

A joker’s cap is in the form of right circular cone of base radius 7 cm and height 24 cm. Find the area of the sheet required to make 10 such caps.

`["Assume "pi=22/7]`

A bus stop is barricaded from the remaining part of the road, by using 50 hollow cones made of recycled cardboard. Each cone has a base diameter of 40 cm and height 1 m. If the outer side of each of the cones is to be painted and the cost of painting is ₹ 12 per m², what will be the cost of painting all these cones?

`("Use "π = 3.14" and take "sqrt1.04= 1.02)`

Find the surface area of a sphere of radius 10.5 cm.

`["Assume "pi=22/7]`

Find the surface area of a sphere of radius 5.6 cm.

`["Assume "pi=22/7]`

Find the surface area of a sphere of radius 14 cm.

`["Assume "pi=22/7]`

Find the surface area of a sphere of diameter 14 cm.

`["Assume "pi=22/7]`

Find the surface area of a sphere of diameter 21 cm.

`["Assume "pi=22/7]`

Find the surface area of a sphere of diameter 3.5 m.

`["Assume "pi=22/7]`

Find the total surface area of a hemisphere of radius 10 cm. [Use π = 3.14]

The radius of a spherical balloon increases from 7 cm to 14 cm as air is being pumped into it. Find the ratio of surface areas of the balloon in the two cases.

A hemispherical bowl made of brass has inner diameter 10.5 cm. Find the cost of tin-plating it on the inside at the rate of ₹ 16 per 100 cm².

`["Assume "pi=22/7]`

Find the radius of a sphere whose surface area is 154 cm².

`["Assume "pi=22/7]`

The diameter of the moon is approximately one-fourth of the diameter of the earth. Find the ratio of their surface area.

A hemispherical bowl is made of steel, 0.25 cm thick. The inner radius of the bowl is 5 cm. Find the outer curved surface area of the bowl.

`["Assume "pi = 22/7]`

A right circular cylinder just encloses a sphere of radius r (see figure). Find

1. surface area of the sphere,
2. curved surface area of the cylinder,
3. ratio of the areas obtained in (i) and (ii).

Find the volume of the right circular cone with radius 6 cm and height 7 cm.

`["Assume "pi=22/7]`

Find the volume of the right circular cone with radius 3.5 cm and height 12 cm.

`["Assume "pi=22/7]`

Find the capacity in litres of a conical vessel with radius 7 cm and slant height 25 cm.

`["Assume "pi=22/7]`

Find the capacity in litres of a conical vessel with height 12 cm and slant height 13 cm.

`["Assume "pi=22/7]`

The height of a cone is 15 cm. If its volume is 1570 cm³, find the radius of its base. [Use π = 3.14]

If the volume of a right circular cone of height 9 cm is 48π cm³, find the diameter of its base.

A conical pit of top diameter 3.5 m is 12 m deep. What is its capacity in kilolitres?

`["Assume "pi=22/7]`

The volume of a right circular cone is 9856 cm³. If the diameter of the base is 28 cm, find

1. height of the cone
2. slant height of the cone
3. curved surface area of the cone

`["Assume "pi=22/7]`

A right triangle ABC with sides 5 cm, 12 cm and 13 cm is revolved about the side 12 cm. Find the volume of the solid so obtained.

A right triangle ABC with sides 5 cm, 12 cm and 13 cm is revolved about the side 12 cm. Find the volume of the solid so obtained.

If the triangle ABC in the above question is revolved about the side 5 cm, then find the volume of the solid so obtained. Find also the ratio of the volumes of the two solids obtained.

A heap of wheat is in the form of a cone whose diameter is 10.5 m and height is 3 m. Find its volume. The heap is to be covered by canvas to protect it from rain. Find the area of the canvas required.

`["Assume "pi=22/7]`

Find the volume of a sphere whose radius is 7 cm.

`["Assume "pi=22/7]`

Find the volume of a sphere whose radius is 0.63 m.

`["Assume "pi=22/7]`

Find the amount of water displaced by a solid spherical ball of diameter 28 cm.

`["Assume "pi=22/7]`

Find the amount of water displaced by a solid spherical ball of diameter 0.21 m.

`["Assume "pi=22/7]`

The diameter of a metallic ball is 4.2 cm. What is the mass of the ball, if the density of the metal is 8.9 g per cm³?

`["Assume "pi=22/7]`

The diameter of the moon is approximately one-fourth of the diameter of the earth. What fraction of the volume of the earth is the volume of the moon?

How many litres of milk can a hemispherical bowl of diameter 10.5 cm hold?

`["Assume "pi=22/7]`

A hemispherical tank is made up of an iron sheet 1 cm thick. If the inner radius is 1 m, then find the volume of the iron used to make the tank.

`["Assume "pi=22/7]`

Find the volume of a sphere whose surface area is 154 cm².

`["Assume "pi=22/7]`

A dome of a building is in the form of a hemisphere. From inside, it was white-washed at the cost of ₹ 4989.60 If the cost of white-washing is ₹ 20 per square meter, find the

1. inside surface area of the dome,
2. volume of the air inside the dome.

`["Assume "pi=22/7]`

Twenty seven solid iron spheres, each of radius r and surface area S are melted to form a sphere with surface area S'. Find the

1. radius r' of the new sphere,
2. ratio of S and S'.

A capsule of medicine is in the shape of a sphere of diameter 3.5 mm. How much medicine (in mm³) is needed to fill this capsule?

`["Assume "pi=22/7]`