Question 63

A sphere of radius 6 cm is melted and recast into spheres of radius 2 cm each. How many such spheres can be made?

Solution

As per the given question,

Radius of larger sphere (R)=6cm and radius of smaller sphere (r)=2cm

We know that, volume of sphere $$=\dfrac{4 \pi R^3}{3}$$

So, $$nV_1=V$$

$$\Rightarrow n\times \dfrac{4 \pi r^3}{3}=\dfrac{4 \pi R^3}{3}$$

$$\Rightarrow n=\dfrac{R^3}{r^3}=\dfrac{6^3}{2^3}$$

$$\Rightarrow n=\dfrac{216}{8}$$

$$\Rightarrow n=27$$

Hence total 27 such sphere can be made.

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