This set of Class 10 Maths Chapter 13 Multiple Choice Questions & Answers (MCQs) focuses on “Conversion of Solid from One Shape to Another”.

1. A metallic sphere whose radius is 5 cm is melted and cast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder.

a) 21.4 cm

b) 43.63 cm

c) 70 cm

d) 72.5 cm^{2}

View Answer

Explanation: Volume of the sphere = volume of the cylinder

\(\frac {4}{3}\)πr

^{3}= πr

^{2}h

\(\frac {4}{3}\) × 3.14 × 5

^{3}= 3.14 × 6

^{2}× h

h = \(\frac {4 \times 3.14 \times 3.14 \times 125}{3.14 \times 36}\)

h = 43.63 cm

2. Three metallic spheres of radius 3 cm, 6 cm, 9 cm are melted into a single sphere. Find the radius of the resulting sphere.

a) 109.4 cm^{3}

b) 4071.48 cm^{3}

c) 1520 cm^{3}

d) 1869.4 cm^{3}

View Answer

Explanation: Volume of the resulting sphere = sum of the volumes of all three spheres

= \(\frac {4}{3}\)π3

^{3}+ \(\frac {4}{3}\)π6

^{3}+ \(\frac {4}{3}\)π9

^{3}

= 113.09 + 904.77 + 3053.62

= 4071.48 cm

^{3}

3. A well of depth 25 m with a radius 4 m is dug from the earth forming a platform of length 28 m and a breadth of 16 m. Find the height of the platform.

a) 2.8 m^{3}

b) 5 m^{3}

c) 5.4 m^{3}

d) 7.2 m^{3}

View Answer

Explanation: Volume of the well = volume of the platform

πr

^{2}h = lbh

3.14 × 4

^{2}× 25 = 28 × 16 × h

h = 2.8 m

^{3}

4. How many coins of 1 cm in diameter and thickness of 1.2 cm need to be melted to form a cuboid with dimensions of 5 cm × 10 cm × 4 cm?

a) 193

b) 213

c) 184

d) 282

View Answer

Explanation: Volume of the cuboid = number of coins(volume of a coin)

lbh = number of coins(πr

^{2}h)

5 × 10 × 4 = number of coins(3.14 × 0.5

^{2}× 1.2)

200 = number of coins(0.94)

number of coins = 213

5. A sphere of radius 14 cm is melted and cast into a number of tiny cones of radius 2.33 cm each and height 6 cm. Find the number of cones that will be formed?

a) 726

b) 816

c) 721

d) 821

View Answer

Explanation: Number of cones(volume of a cone) = volume of sphere

number of cones(\(\frac {1}{3}\)πr

^{2}h) = \(\frac {4}{3}\)πr

^{3}

number of cones(\(\frac {1}{3}\) × 3.14 × 2.33

^{2}× 6) = \(\frac {4}{3}\) × 3.14 × 14

^{3}

number of cones(14) = 11488.21

number of cones = 821

6. How many cylinders having 2.1 cm of radius and 1.4 cm of height can be made out of a cuboid metal box having dimensions 33 cm, 21 cm, 10.5 cm?

a) 152

b) 154

c) 844

d) 841

View Answer

Explanation: Number of cylinders(volume of a cylinder) = volume of a cuboid

Number of cylinders (πr

^{2}h) = lbh

Number of cylinders (3.14 × 1.4

^{2}× 1.4) = 33 × 21 × 10.5

Number of cylinders = 844

7. A sphere having a radius of 3 cm is melted and elongated into a wire having a circular cross-section of radius 0.1 cm. Find the length of the wire?

a) 2400 cm

b) 3100 cm

c) 1200 cm

d) 3600 cm

View Answer

Explanation: Volume of the wire = volume of the sphere

πr

^{2}h = \(\frac {4}{3}\)πr

^{3}

3.14 × 0.1

^{2}× h = \(\frac {4}{3}\) × 3.14 × 27

h = 3600 cm

8. A cylindrical hole of depth 20 m with a radius 5 m is dug from the earth forming a platform of length 14 m and a breadth of 12 m. Find the height of the platform.

a) 8.34 m^{3}

b) 11.84 m^{3}

c) 7.64 m^{3}

d) 9.34 m^{3}

View Answer

Explanation: Volume of the cylindrical hole = volume of the platform

πr

^{2}h = lbh

3.14 × 5

^{2}× 20 = 14 × 12 × h

h = 9.34 m

^{3}

9. What is the formula to find the rise in the water level when ‘x’ spherical balls are dropped into a cylindrical beaker?

a) \(\frac {Volume \, of \, ‘x’ \, spherical \, balls}{Base \, area \, of \, cylinder}\)

b) \(\frac {Volume \, of \, ‘x’ \, spherical \, balls}{2(Base \, area \, of \, cylinder)}\)

c) The volume of the cylinder + volume of the beaker

d) The volume of the cylinder – 2(volume of the beaker)

View Answer

Explanation: To find the rise in the water level we require the volume of ‘x’ spherical balls and the base area of the cylinder

Rise in the water level = \(\frac {Volume \, of \, ‘x’ \, spherical \, balls}{Base \, area \, of \, cylinder}\)

10. A metallic sphere whose radius is 4 cm is melted and cast into the shape of a right circular cone of radius 7 cm. Find the height of the cylinder?

a) 14.48 cm

b) 22.36 cm

c) 16.40 cm

d) 20.32 cm

View Answer

Explanation: Volume of the sphere = volume of the cone

\(\frac {4}{3}\) πr

^{3}= \(\frac {1}{3}\) πr

^{2}h

\(\frac {4}{3}\) × 3.14 × 4

^{3}= 3.14 × 7

^{2}× h

h = \(\frac {4 \times 3.14 \times 3.14 \times 64}{3.14 \times 49}\)

h = 16.40 cm

11. Three metallic spheres of radius 2 cm, 4 cm, 8 cm are melted into a single sphere. Find the radius of the resulting sphere.

a) 1009.4 cm^{3}

b) 2446.25 cm^{3}

c) 1520 cm^{3}

d) 2869.4 cm^{3}

View Answer

Explanation: Volume of the resulting sphere = sum of the volumes of all three spheres

= \(\frac {4}{3}\)π2

^{3}+ \(\frac {4}{3}\)π4

^{3}+ \(\frac {4}{3}\)π8

^{3}

= \(\frac {4}{3}\) × 3.14(2

^{3}+ 4

^{3}+ 8

^{3})

= 2446.25 cm

^{3}

**Sanfoundry Global Education & Learning Series – Mathematics – Class 10**.

To practice all chapters and topics of class 10 Mathematics, __ here is complete set of 1000+ Multiple Choice Questions and Answers__.

**If you find a mistake in question / option / answer, kindly take a screenshot and email to [email protected]**

**Related Posts:**

- Practice Class 9 Mathematics MCQs
- Check Class 10 - Mathematics Books
- Practice Class 8 Mathematics MCQs