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

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Solution

Q.
12 spheres 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:

1 $\sqrt{3} cm$

2 2 cm

3 3 cm

4 4 cm

Ans.
(4)

$R a d i u s o f c y l i n d e r = \frac{16}{2} = 8 cm$

Let r cm be the radius of each sphere.

hen one solid shape is converted into another, the volume remains the same

$∴ Volume of the solid cylinder = 12 \times volume of one sphere$

$π \times (8)^{2} \times 2 = 12 \times \frac{4}{3} π r^{3}$

$128 = 16 r^{3} \Rightarrow r^{3} = 8 \Rightarrow r = 2 cm$

$Diameter of sphere = 2 r = 2 \times 2 = 4 cm$

$∴ Option (d) is correct.$

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