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.
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.

For side of the equator,

Span, r = 8 cm

We realize that,

volume of side of the equator = 2/3 πr3, where, r = sweep of half of the globe

In this way, we get,

Volume of given side of the equator \[=\text{ }2/3\text{ }\times \text{ }\pi \text{ }\times \text{ }83\text{ }=\text{ }\left( 1024/3 \right)\text{ }\pi \text{ }cm3\]

Presently,

For the cone that is reevaluated from a half of the globe,

Base span, r = 6 cm

We likewise realize that,

Volume of cone = 1/3 πr2h, where, r is base span and h is the tallness of the cone.

In this way, we get,

Volume of cone \[=\text{ }1/3\text{ }\pi \left( 6 \right)2h\text{ }=\text{ }12\pi h\]

As indicated by the inquiry, we realize that,

The volume stays same, when a body is transformed to another body

Volume of chamber = Volume of cone

12πh = 1024π/3

h = 28.44 cm