Class 9 Practice Level 3 – Set 1 – Surface Areas and Volumes

Total questions: 15

A conical vessel with a base radius of 5 cm and height of 12 cm is completely filled with water. The water is then poured into a cylindrical vessel with a base radius of 10 cm. What is the height of the water in the cylindrical vessel?

Topic: Volume of Cones

1 cm

2 cm

3 cm

4 cm

None

A hemisphere of radius 7 cm is placed on top of a cylinder with the same radius and height of 10 cm. What is the total surface area of the resulting solid?

Topic: Surface Area of Hemispheres

462 cm²

616 cm²

770 cm²

924 cm²

None

A solid metallic sphere of radius 9 cm is melted and recast into 27 smaller spheres of equal size. What is the radius of each smaller sphere?

Topic: Volume of Spheres

• 2 cm

• 3 cm

• 4 cm

• 5 cm

None

A right circular cone has a base diameter of 14 cm and a height of 24 cm. A plane parallel to the base cuts the cone at half its height. What is the ratio of the curved surface area of the smaller cone to the original cone?

Topic: Surface Area of Cones

1:4

1:2

1:3

1:5

None

A cylindrical tank with a diameter of 20 m is filled with water to a height of 5 m. If the water is pumped out at a rate of 50 m³/min, how long will it take to empty the tank?

Topic: Volume of Cylinders

20 minutes

25 minutes

30 minutes

35 minutes

None

A spherical ball with a diameter of 14 cm is cut into two equal hemispheres. What is the increase in the total surface area?

Topic: Volume of Spheres

196π cm²

154π cm²

98π cm²

42π cm²

None

A solid hemisphere is placed on top of a solid cylinder with the same base radius. If the radius is 7 cm and the total height of the solid is 21 cm, what is the volume of the entire solid?

Topic: Volume of Hemispheres

4312 cm³

3465 cm³

2643 cm³

2145 cm³

None

A cone is divided into two parts by a plane parallel to the base, resulting in a smaller cone and a frustum. If the volume of the smaller cone is 1/8th of the original cone, what is the ratio of the surface area of the smaller cone to the original cone?

Topic: Surface Area of Cones

1:2

1:4

1:3

1:8

None

A cuboid is melted and recast into a cube. If the original dimensions of the cuboid were 15 cm x 10 cm x 5 cm, what is the side length of the cube?

Topic: Volume of Cuboids

8 cm

10 cm

12 cm

14 cm

None

10.

Two spheres have surface areas in the ratio 4:9. What is the ratio of their volumes?

Topic: Surface Area of Spheres

2:3

4:9

8:27

16:81

None

11.

A cone with a height of 12 cm and a base radius of 6 cm is divided into two parts by a plane parallel to the base, such that the height of the smaller cone is 4 cm. What is the volume of the frustum formed?

Topic: Volume of Cones

108π cm³

192π cm³

252π cm³

288π cm³

None

12.

A cylindrical tank with a height of 10 m is half-filled with water. If the surface area of the water in the tank is 200 m², what is the radius of the tank?

Topic: Surface Area of Cylinders

4 m

5 m

6 m

7 m

None

13.

A spherical balloon is being inflated so that its radius increases at a rate of 2 cm/min. How fast is the volume of the balloon increasing when the radius is 5 cm?

Topic: Volume of Spheres

100π cm³/min

200 cm³/min

300π cm³/min

400π cm³/min

None

14.

A cone is inscribed in a hemisphere such that the base of the cone coincides with the base of the hemisphere. If the radius of the hemisphere is 6 cm, what is the total surface area of the cone?

Topic: Surface Area of Cones

108π cm²

150π cm²

216π cm²

300π cm²

None

15.

A cone with a slant height of 13 cm is filled with water to $ \displaystyle \dfrac{1}{3}$ of its height. If the base radius of the cone is 5 cm, what is the volume of the water in the cone?

Topic: Volume of Cones

100π cm³

150π cm³

200π cm³

250π cm³

None

1 out of 15

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Class 9 Practice Level 3 – Set 1 – Surface Areas and Volumes

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