Question

A hemisphere of lead of radius 6 cm is cast into a right circular cone of height 75 cm. Find the radius of the base of the cone.

Answer 1

We have,

Radius of the hemisphere, R = 6 cm and 

Height of the cone, h = 75 cm

Let the radius of the base of the cone be r.

Now,

Volume of the cone = Volume of the hemisphere

`=> 1/3 pi"r"^2"h" = 2/3pi"R"^3`

`=> "r"^2 = (2"R"^3)/"h"`

`=> "r"^2 = 5.76 `

`=>"r"^2 = sqrt(5.76)`

∴ r = 2.4 cm

So, the radius of the base of the cone is 2.4 cm.