Question

A sphere of radius $4$ cm has the same volume as that of a cone with a circular base of radius $4$ cm.The height of the cone is

• A. $12$ cm
• B. $16$ cm
• C. $20$ cm
• D. $24$ cm

Answer 1

The correct option is B $16$ cm

Radius of sphere $=$ radius of cone $=4$ cm
Volume of cone $=$ $\frac{1}{3}\pi r^{2}h$
Volume of Sphere $=$ $\frac{4}{3}\pi r^3$
Volume of cone $=$ Volume of Sphere
$\Rightarrow \frac{1}{3}\pi r^{2}h$ $=$ $\frac{4}{3}\pi r^3$
$\Rightarrow h=4r$
$\Rightarrow h=16$ cm