Question

The radius of a solid sphere is $7$ cm. If the solid sphere is melt to form small spheres of radius $3.5$ cm. Then how many small spheres can be formed?

Answer 1

Given the radius of the solid sphere is $7$ cm.

Then its volume is $\frac{4}{3}\times \pi \times 7^3$ cm${}^3$.

Also given the radius of the small sphere is $3.5$ cm.

Then the volume of the small sphere is $\frac{4}{3}\times \pi \times {\left(\frac{7}{2}\right)}^3$ cm${}^3$.

Let there be $n$ small spheres.

Then equating the volumes of $n$ spheres to the bigger spheres we get,

$\frac{4}{3}\times \pi \times 7^3=$ $n\times \frac{4}{3}\times \pi \times {\left(\frac{7}{2}\right)}^3$

or, $\frac{4}{3}\times \pi \times 7^3=$ $n\times \frac{4}{3}\times \pi \times \frac{7^3}{8}$

or, $n=8$.