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. $1:2$
• B. $2\sqrt{3}:\sqrt{5}$
• C. $2\sqrt{2}:3$
• D. $\sqrt{2}:\sqrt{3}$

Answer 1

The correct option is D $\sqrt{2}:\sqrt{3}$

Given: Radius of the hemisphere = 21 cm
Height of the cone is = 42 cm
Let the radius of the cone be r.
Volume of cone = Volume of hemisphere
$\frac{1}{3}\pi \times r^2\times 42=\frac{2}{3}\pi \times 21\times 21\times 21$
$r^2={21}^2$
r = 21 cm