Question

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

Answer 1

In the given problem, we have a lead hemisphere which is remolded into a right circular cone.

Here,

Radius of the hemisphere (r_h) = 7 cm

Height of the cone (h) = 49 cm

So, let the base radius of the cone (r_c) = x cm

Now, the volume of the hemisphere will be equal to volume of the volume of the cone.

So, we get,

Volume of the hemisphere = volume of the cone

Further, solving for x

Further,

Therefore, base radius of the cone is .