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

B

2 cm

C

3 cm

D

4 cm

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=12812π⇒r3=8⇒r=2 cm ∴ diameter of the sphere=4 cm Mathematics

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