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

Question

Philoid · Accepted Answer

For hemisphere,

Radius, r = 8 cm

As we know,

Volume of hemisphere

Where, r = radius of hemisphere

Volume of given hemisphere

For cone that is recast from hemisphere,

Base radius, r = 6 cm

We know that,

volume of cone

Where, r is base radius and h is the height of the cone.

Now,

Volume of cone

As 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