Question

A hemisphere is melted and used some part of it to make a right circular cone whose radius and height are equal to the radius of the hemisphere. The volumes of hemisphere and cone are in the ratio 4:1.

• A. True
• B. False

Answer 1

The correct option is B False

We know that,
$\text{Volume of hemisphere}$
$=\frac{2}{3}\pi r^3$
$\text{Volume of the recasted cone}$
$=\frac{1}{3}\pi R^2\left(H\right)$

Given that,
Height of the cone = Radius of the hemisphere
$\Rightarrow H=r$
Radius of cone = Radius of hemisphere
$\Rightarrow R=r$

Now, Volume of cone
$=\frac{1}{3}\pi \left(r^2\right)\times r$
$=\frac{1}{3}\pi r^3$

$\text{The ratio of their volumes}$

$=\frac{Volumeofhemisphere}{Volumeofcone}$

$=\frac{\frac{2}{3}\pi r^3}{\frac{1}{3}\pi r^3}$

$=2:1$