Question

A solid sphere of radius $15cm$ is melted and react into solid right circular cones of radius $2.5cm$ and height $8cm$. Calculate the number of cones recast.

Answer 1

Radius of a solid sphere, $r=15cm$

Volume of a solid sphere $=\frac{4}{3}\pi r^3$

$=\frac{4}{3}\times \pi (15{)}^{3}c{m}^3$.

Now, radius of right circular cone $=2.5cm$
and height, $h=8cm$.

Volume of right circular cone $=\frac{1}{3}\pi r^{2}h$

$=\frac{1}{3}\pi (2.5{)}^2\times 8$

$\therefore$ The number of cones $=\frac{\text{Volume of a sphere}}{\text{Volume of a cone}}$

$=\frac{\frac{4}{3}\pi \times (15{)}^3}{\frac{1}{3}\pi (2.5{)}^2\times 8}$

$=\frac{15\times 15\times 15}{2.5\times 2.5\times 2}$

$=270$.