Class 10 Practice Level 3 – Set 1 – Surface Areas and Volumes

Total questions: 15

A solid metal sphere of radius 6 cm is melted and recast into smaller spheres, each of radius 2 cm. How many smaller spheres can be made?

Topic: Volume of a Sphere

None

A hemispherical bowl is made of steel and has an outer radius of 7 cm and a thickness of 1 cm. What is the total surface area of the bowl?

Topic: Surface Area of a Hemisphere

770 cm²

770π cm²

154π cm²

616π cm²

None

A cylindrical tank with radius 5 m is filled with water to a height of 9 m. If the water is emptied into a cuboidal tank of dimensions 10 m x 6m x 4.5 m, will the water overflow?

Topic: Volume of a Cylinder

Yes

None

A right circular cone is inscribed in a sphere of radius 10 cm such that the cone's vertex coincides with the center of the sphere. Find the total surface area of the cone.

Topic: Surface Area of a Cube

300π cm²

400π cm²

500π cm²

600π cm²

None

Two hemispheres of radius 7 cm are joined together along their flat faces. Find the volume of the resulting solid.

Topic: Volume of a Hemisphere

3584 cm³

1436 cm³

4312 cm³

6160 cm³

None

A spherical balloon is inflated such that its radius increases from 7 cm to 14 cm. By what factor does the surface area increase?

Topic: Surface Area of a Sphere

None

A cone of height 12 cm is carved out from a cylinder of height 12 cm and radius 6 cm. What is the volume of the remaining solid?

Topic: Volume of a Cone

432π cm³

288π cm³

144π cm³

216π cm³

None

A hemispherical dome has a base diameter of 14 m. It needs to be painted, and the cost of painting is 12 per square meter. What is the total cost of painting the dome?

Topic: Surface Area of a Hemisphere

₹1848

₹1232

₹2464

₹3696

None

The volume of a sphere is 38808 cm³. Find its surface area.

Topic: Volume of a Sphere

1256 cm²

2827 cm²

4524 cm²

6160 cm²

None

10.

A cylindrical water tank with a diameter of 10 m and height 15 m is to be coated with a protective layer on the outside. What is the area to be coated?

Topic: Surface Area of a Cylinder

300π m²

450π m²

500π m²

750π m²

None

11.

A solid hemisphere of radius 14 cm is melted and recast into a cone with a radius of 7 cm. Find the height of the cone.

Topic: Volume of a Hemisphere

56 cm

48 cm

36 cm

24 cm

None

12.

A cone is formed by revolving a right-angled triangle with base 9 cm and height 12 cm about its height. Find the surface area of the cone.

Topic: Surface Area of a Cone

132π cm²

225π cm²

252π cm²

315π cm²

None

13.

A spherical tank has a capacity of 5000 liters. Find the radius of the tank in meters.

Topic: Volume of a Sphere

0.95 m

1.07 m

1.33 m

1.50 m

None

14.

A sphere is cut into two equal halves. Find the total surface area of one half, including the base. The radius of the sphere is 10 cm.

Topic: Surface Area of a Sphere

400π cm²

600π cm²

700π cm²

900π cm²

None

15.

A metal hemisphere of radius 5 cm is melted and recast into a sphere. Find the radius of the sphere.

Topic: Volume of a Hemisphere

2.5 cm

3 cm

4 cm

5 cm

None

1 out of 15

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Class 10 Practice Level 3 – Set 1 – Surface Areas and Volumes

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