Question

A certain number of metallic cones, each of radius $2cm$ and height $3cm$ are melted and recast into a solid sphere of radius $6cm$. Find the number of cones

Answer 1

Let number of cones $=n$
Volume of cones $=$ Volume of sphere
$\frac{1}{3}\pi r^{2}h\times n=\frac{4}{3}\pi r^3$
$n\times \frac{1}{3}\pi \times 2^2\times 3=\frac{4}{3}\pi \times 6^3$
$n=\frac{216}{3}$
$n=72$
Hence, no. of cones $=72$