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Question

12 spheres of the same size are made by melting a solid cylinder of diameter 16 cm and height 2 cm. 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 diameter of the cylinder = 16 cm R=8 cm 
Volume of the cylinder of radius R and height h
 =πR2×h=π×82×2=128π cm3
As this volume is filled into 12 identical spheres, Volume of one sphere=Volume of the cylinder12

Let the radius of the sphere be r
43πr3=12812πr3=8r=2 cm
diameter of the sphere=4 cm


Mathematics

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