Class 9 Practice Level 3 – Set 2 – Surface Areas and Volumes

Total questions: 15

A sphere is inscribed in a cube such that it touches all the faces of the cube. If the surface area of the sphere is 154 cm², what is the surface area of the cube?

Topic: Surface Area of Spheres

144 cm²

196 cm²

294 cm²

256 cm²

None

A right circular cone is divided into two parts by a plane parallel to the base, resulting in a smaller cone and a frustum. If the smaller cone has a height of 6 cm and the original cone has a height of 18 cm, what is the volume of the frustum?

Topic: Volume of Cones

648π cm³

756π cm³

864π cm³

972π cm³

None

A hollow hemisphere has an outer radius of 10 cm and a thickness of 2 cm. What is the area of the material used to make the hemisphere?

Topic: Surface Area of Hemispheres

300π cm²

350π cm²

400π cm²

500π cm²

None

A solid sphere of radius 10 cm is melted and recast into a right circular cone with the same radius. What is the height of the cone?

Topic: Volume of Spheres

20 cm

30 cm

40 cm

50 cm

None

A cuboid has dimensions 15 cm x 10 cm x 8 cm. If each dimension is increased by 50%, what is the percentage increase in the surface area?

Topic: Surface Area of Cuboids

75%

100%

125%

150%

None

A cone with a height of 12 cm is melted and recast into a cone with double the radius of the original cone. What is the height of the new cone?

Topic: Volume of Cones

3 cm

6 cm

12 cm

24 cm

None

A cylindrical tank is open at the top and has a height of 10 m and a radius of 5 m. What is the total surface area of the tank that needs to be painted if only the outer surface is to be painted?

Topic: Surface Area of Cylinders

100π m²

125π m²

200π m²

250π m²

None

A sphere with a radius of 5 cm is divided into two equal hemispheres. What is the total surface area of the two hemispheres, including their bases?

Topic: Volume of Spheres

150π cm²

200π cm²

250π cm²

300π cm²

None

A cone is cut by a plane parallel to the base, and the upper part is removed. If the volume of the removed part is $ \displaystyle \dfrac{1}{8}$th of the original cone, what is the ratio of the height of the original cone to the height of the remaining frustum?

Topic: Surface Area of Cones

1:1

2:1

3:1

4:1

None

10.

A hemisphere has a volume of 288 cm³. What is its curved surface area?

Topic: Volume of Hemispheres

72π cm²

108π cm²

144π cm²

216π cm²

None

11.

A cuboid has dimensions 20 cm x 15 cm x 10 cm. If it is painted on all six faces, what is the area of the largest face that is not painted?

Topic: Surface Area of Cuboids

150 cm²

200 cm²

250 cm²

300 cm²

None

12.

A sphere is inscribed in a cube. If the volume of the sphere is $ \displaystyle \dfrac{4}{3}\pi $, what is the volume of the cube?

Topic: Volume of Spheres

$ \displaystyle {2{{r}^{3}}}$

$ \displaystyle {3{{r}^{3}}}$

$ \displaystyle {4{{r}^{3}}}$

$ \displaystyle {8{{r}^{3}}}$

None

13.

A cylindrical vessel with a height of 8 m and a radius of 3 m is filled with water. If the water is transferred into a cone with the same radius, what will be the height of the water in the cone?

Topic: Surface Area of Cylinders

6 m

8 m

10 m

24 m

None

14.

A solid hemisphere is melted and recast into 8 identical smaller hemispheres. What is the ratio of the radius of the original hemisphere to the radius of the smaller hemispheres?

Topic: Volume of Hemispheres

1:2

2:1

2:3

1:4

None

15.

A cone has a base radius of 7 cm and a height of 24 cm. If a plane cuts the cone parallel to the base at half the height, what is the ratio of the surface area of the smaller cone to the original cone?

Topic: Surface Area of Cones

1:4

1:2

1:3

1:6

None

1 out of 15

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Class 9 Practice Level 3 – Set 2 – Surface Areas and Volumes

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