Question

A solid metallic hemisphere of radius $8$ cm is melted and recast into a right circular cone of base radius $6$ cm. Determine the height of the cone.(Insert answer in nearest integer)

Answer 1

According to the question, we can write

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

$\therefore \frac{2}{3}\pi 8^3=\frac{1}{3}\pi 6^{2}h$

$\therefore h=\frac{1024}{36}=28.44$