Question

A hemisphere of lead of radius $$8\ cm$$ is cast into a right circular cone of base radius $$6\ cm$$. Determine the height of the cone, correct to two places of decimals.

Answer 1

Radius of hemisphere $$=8cm$$
and Radius of right circular cone $$=6cm$$
According to question,
Volume of the hemisphere = Volume of cone
$$\Rightarrow \ \dfrac {2}{3}\pi r^3=\dfrac {1}{3}\pi R^2 h$$
$$\Rightarrow \ \dfrac {2}{3}\times \pi \times 8\times 8\times 8= \dfrac {1}{3}\times \pi \times 6\times 6\times h$$
$$\Rightarrow \ \dfrac {1024}{36}=h$$
$$\Rightarrow \ h=28.44cm$$