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Question

# A sphere of radius 4 cm is melted and recast into the shape of a cylinder of radius 8 cm. What is the height of the cylinder formed?

A

1.33 cm

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B

3.21 cm

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C

0.95 cm

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D

2.22 cm

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Solution

## The correct option is A 1.33 cm Given, radius of sphere, r = 4 cm radius of cylinder, R = 8 cm Let height of the cylinder be h cm. Volume of sphere =43πr3=43π(4)3=2563π cm3 Volume of the cylinder =πR2h=π×(8)2×h=64πh In the process of melting and recasting, the volume of the solids remain the same. So, volume of the sphere = volume of the cylinder ⇒2563π=64πh ⇒2563=64h ⇒h=2563×64 ⇒h=1.33 cm Therefore, height of the cylinder = 1.33 cm

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