Question

If a hemisphere of radius 21 cm is melted and recast to form a cone of height 42 cm, then the radius of cone is ___.

• A. 10 cm
• B. 16 cm
• C. 14 cm
• D. 21 cm

Answer 1

The correct option is D 21 cm

Given: Radius of the hemisphere = 21 cm
Height of the cone = 42 cm
Let the radius of the cone be $r$.

Here, a hemisphere is melted and recast into a cone.
During recasting, volume remains the same. So,
Volume of cone = Volume of hemisphere
We know that, volume of cone =$\frac{1}{3}\pi \times (radius{)}^2\times height$
and volume of hemisphere = $\frac{2}{3}\pi (radius{)}^3$

$\Rightarrow \frac{1}{3}\pi \times r^2\times 42=\frac{2}{3}\pi \times 21\times 21\times 21$
$\Rightarrow r^2={21}^2$
$\Rightarrow r=21cm$