1)

A hemisphere of radius 6 cm is cast into a right circular cone of height 75 cm.What is the radius of the base of cone?


A) 1.4 cm

B) 2.4 cm

C) 2.6 cm

D) 3 cm

Answer:

Option B

Explanation:

Let r1 be the radius of the hemishere and r2 be the radius of the cone.

Volume of hemisphere = Volume of cone

$\frac{2}{3}\pi (r1)^{3}=\frac{1}{3}\pi (r2)^{2}h$

$\Rightarrow \frac{2}{3}\pi (6)^{3}=\frac{1}{3}\pi (r2)^{2}\times 75 $ $\Rightarrow (r2)^{2}=\frac{3}{75} \times \frac{2}{3}\times (6^{3})$

$=\frac{2}{25\times 3} \times  6\times 6\times 6$ $\Rightarrow r2=\frac{12}{5}=2.4 cm$