Question

A solid metallic hemisphere of radius 8 cm is melted and recasted into a right circular cone of base radius 6 cm. Determine the height of the cone.

Answer 1

For hemisphere,

Radius, r = 8 cm

We know that,

Volume of hemisphere = `2/3 π"r"^3`, where, r = radius of hemisphere

So, we get,

Volume of given hemisphere = `2/3 xx π xx 8^3`

= `(1024/3)π  "cm"^3`

Now,

For the cone that is recast from a hemisphere,

Base radius, r = 6 cm

We also know that,

Volume of cone = `1/3 π"r"^2"h"`, where, r is base radius and h is the height of the cone.

So, we get,

Volume of cone = `1/3 π(6)^2"h"` = 12πh

According to the question, we know that,

The volume remains same, when a body is reformed to another body

Volume of cylinder = Volume of cone

12πh = `(1024π)/3`

h = 28.44 cm