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Q.

An iron sphere of radius 14 cm is melted. The spheres each of diameter 7 cm can be made out of it is

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a

10

b

64

c

88

d

49

answer is D.

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Detailed Solution

n x volume of sphere = volume of bigger sphere

$\begin{array}{l} \Rightarrow n \cdot \frac{4}{3} π r^{3} = \frac{4}{3} π R^{3} \\ \Rightarrow n = \frac{R^{3}}{r^{3}} = \frac{14 \times 14 \times 14}{\frac{7}{2} \times \frac{7}{2} \times \frac{7}{2}} \\ \Rightarrow n = 64 \end{array}$

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