Question

A solid sphere of radius $3cm$ is melted and then cast into small spherical balls each of diameter $0.6cm$. Find the number of balls thus obtained.

Answer 1

Let the total number of balls be $x$

Volume of the solid sphere $=\frac{4}{3}\pi r^3=\frac{4}{3}\pi \times 3^3{cm}^3=36\pi {cm}^3$

Radius of spherical ball $=\frac{0.6}{2}cm=0.3cm$

Volume of a spherical ball $=\frac{4}{3}\pi \times {\left(0.3\right)}^3{cm}^3$

$=\frac{4}{3}\pi \times \frac{3}{10}\times \frac{3}{10}\times \frac{3}{10}{cm}^3=\frac{36\pi }{1000}{cm}^3$

Volume of $x$ spherical balls $=\frac{36\pi }{1000}x{cm}^3$

Clearly volume of the solid spheres = volume of $x$ spherical balls

$36\pi =\frac{36\pi }{1000}x\Rightarrow x=1000$

Hence $1000$ spherical balls are obtained by melting the given solid sphere.