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12 solid spheres of the same radii are made by melting a solid metallic cylinder of base diameter 2cm and height 16cm. Find the diameter of each sphere.

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5 cm

1 cm

3 cm

2 cm

answer is D.

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Detailed Solution

Given that, 12 solid spheres of same radii are made from a cylinder of diameter =2cm and height =16cm.
Therefore, Volume of cylinder = Volume of 12 spheres.
Volume of cylinder = 12

\times

Volume of 1 sphere.
We know that,
Volume of cylinder

= π r 2 h

,
Volume of sphere

= 43 π r 3 .

Now,

π × (Radius cylinder) 2 × Height of cylinder = 12 × 43 π (Radius sphere) 3 ⇒ π × 1 × 16 = 12 × 43 π (Radius sphere) 3 ⇒ 16 π 16 π = (Radius sphere) 3 ⇒ (Radius sphere) 3 = 1 ⇒ Radius sphere = 1

Therefore, the diameter of sphere = 2

\times

(radius of sphere) = 2 cm.
The correct option is (4).

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