# A hemisphere of the lead of radius 7 cm is cast into a right circular cone of height 49 cm.

Question:

A hemisphere of the lead of radius 7 cm is cast into a right circular cone of height 49 cm. Find the radius of the base.

Solution:

Given

Radius of the hemisphere = Volume of cone

$\frac{2}{3} \pi r_{1}^{3}=\frac{1}{3} \pi r_{2}^{2} h$

$\frac{2}{3} \times 7^{3}=\frac{1}{3} r_{2}^{2} \times 49$

$r_{2}^{2}=\frac{2 \times 7 \times 7 \times 7 \times 3}{3 \times 49}$

$r_{2}^{2}=2058147$

r2 = 3.47 cm

Therefore radius of the base = 3.74 cm