Question

The base radius and height of a right circular solid cone are $12cm$ and $24cm$, respectively. It is melted and recast into spheres of diameter $6cm$ each. Find the number of spheres so formed.

• A. $48$
• B. $40$
• C. $32$
• D. $24$

Answer 1

The correct option is C $32$

Radius of a right circular solid cone $=12cm$
Height of a right circular solid cone $=24cm$
Sphere diameter $=6cm$
Volume of right circular solid cone $=V=N\times$ Volume of sphere
$V=\frac{1}{3}\pi r^{2}h=N\times \frac{4}{3}\pi r^3$
$\frac{1}{3}\times {12}^2\times 24=N\times \frac{4}{3}{3}^3$
$N=32$