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Question

12 sphere of the same size are made from melting a solid cylinder of 16 cm diameter and 2 cm height. The diameter of each sphere is:

A
3 cm
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B
2 cm
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C
3 cm
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D
4 cm
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Solution

The correct option is D 4 cm
Given that, 12 spheres of same size are made by melting a cylinder of 16 cm diameter and 2 cm height.
to find out: The diameter of each sphere.

Since, the spheres are made by melting the cylinder, the volume of 12 spheres = the volume of cylinder
We know that, volume of cylinder =πr2h
and volume of sphere =43πr3

12×(43πr3)=π(8)2×2=128π

r3=128×312×4=8

r3=(2)3

r=2 cm

Hence, diameter of each sphere =2r=4 cm.
Hence, option D is correct.

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