Question

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

• A. 64
• B. 32
• C. 16
• D. 20

Answer 1

The correct option is B 32

Volume of the cone $=\frac{1}{3}\pi (12{)}^2\times 24=1152\pi c{m}^3$
Radius of each spherical ball
$=\frac{6}{2}=3cm$
Volume of spherical ball
= $\frac{4}{3}\pi r^3$ = $\frac{4}{3}\pi (3{)}^3$
Number of spherical balls
$=\frac{3\times 1152\pi }{4\pi (3{)}^3}=32$