Class 10 Practice Level 3 – Set 2 – Surface Areas and Volumes

Total questions: 15

A solid metal cylinder of radius 5 cm and height 14 cm is melted and recast into 20 smaller identical cylinders. If the height of each smaller cylinder is 7 cm, find the radius of each smaller cylinder.

Topic: Volume of a Cylinder

2.5 cm

3 cm

4 cm

5 cm

None

A solid sphere of radius 12 cm is cut into 8 identical pieces. What is the surface area of each piece?

Topic: Surface Area of a Sphere

144π cm²

288π cm²

432π cm²

576π cm²

None

A cone of base radius 6 cm and height 12 cm is divided into two parts by a plane parallel to its base. If the volume of the smaller cone is $ \displaystyle \dfrac{{1}}{8}$ of the larger cone, find the height of the smaller cone

Topic: Volume of a Cone

3 cm

4 cm

6 cm

8 cm

None

A hemispherical bowl has an outer diameter of 20 cm and a thickness of 1 cm. Find the outer surface area of the bowl.

Topic: Surface Area of a Hemisphere

300π cm²

396π cm²

500π cm²

600π cm²

None

A spherical ball of diameter 28 cm is melted and recast into smaller balls of diameter 7 cm. How many smaller balls can be made?

Topic: Volume of a Sphere

None

A cylinder has a height of 14 cm and a diameter of 10 cm. It is completely filled with water and then tilted to an angle of 30°. What will be the exposed surface area of the water?

Topic: Surface Area of a Cylinder

100π cm²

150π cm²

200π cm²

250π cm²

None

A conical vessel has a height of 24 cm and a base radius of 9 cm. It is filled with water and then emptied into another conical vessel with a height of 48 cm and a base radius of 12 cm. What will be the height of the water level in the second vessel?

Topic: Volume of a Cone

8 cm

12 cm

18 cm

24 cm

None

A hollow hemispherical shell with an outer radius of 10 cm and inner radius of 9 cm is to be painted. What is the area to be painted?

Topic: Surface Area of a Hemisphere

361π cm²

100π cm²

209π cm²

190π cm²

None

A spherical ball is dropped into a cylindrical container of diameter 10 cm, filled with water to a height of 15 cm. If the ball is fully submerged, the water level rises by 2 cm. Find the radius of the ball.

Topic: Volume of a Sphere

1.5 cm

2 cm

2.5 cm

3 cm

None

10.

A conical tent has a radius of 7 m and a height of 24 m. Find the slant height of the tent and the canvas required to cover it, if the base is left open.

Topic: Surface Area of a Cone

12 m, 154 m²

25 m, 550 m²

30 m, 660 m²

25 m, 385 m²

None

11.

Two hemispheres of radii 6 cm and 8 cm are combined to form a solid. Find the volume of the resulting solid.

Topic: Volume of a Hemisphere

1080 cm³

1264 cm³

1640 cm³

1792 cm³

None

12.

A sphere is inscribed in a cube of edge 10 cm. Find the ratio of the surface area of the sphere to the surface area of the cube

Topic: Surface Area of a Sphere

2:3

3:4

4:5

5:6

None

13.

A cone is formed by rotating a right-angled triangle with legs of length 5 cm and 12 cm about one of its legs. Find the volume of the cone formed.

Topic: Volume of a Cone

100π cm³

180π cm³

240π cm³

300π cm³

None

14.

A hollow hemisphere of outer radius 10 cm and thickness 2 cm is made of metal. Find the volume of the metal used.

Topic: Surface Area of a Hemisphere

1672 cm³

2048 cm³

2560 cm³

3184 cm³

None

15.

A sphere of radius 4 cm is melted and recast into 8 smaller identical spheres. Find the radius of each smaller sphere.

Topic: Volume of a Sphere

2 cm

2.5 cm

3 cm

3.5 cm

None

1 out of 15

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Class 10 Practice Level 3 – Set 2 – Surface Areas and Volumes

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