Question

If a solid sphere of $3cm$ radius is melted and re-casted into a right circular cone whose base radius is same as that of the sphere, the height of the cone will be:

• A. $8cm$
• B. $12cm$
• C. $6cm$
• D. $5cm$

Answer 1

The correct option is B $12cm$

Volume of the sphere of radius $3cm=\frac{4}{3}\pi \times {\left(3\right)}^3$
$=\frac{4}{3}\pi \times 27cucm$
Suppose the height of the cone= h cm
$\therefore$ Volume of the cone having base radius equal to that of the sphere
$\frac{1}{3}h{\left(3\right)}^2\times h$
$\because$ Volume of the cone $=$ Volume of the sphere
$\therefore \frac{1}{3}\pi {\left(3\right)}^2\times h=\frac{4}{3}\pi \times 27\Rightarrow h=12cm$
$\therefore$ Height of the cone $=12cm$