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

Explanation

Given :
Radius of hemisphere, `r = 7 cm`
Height of a right circular cone ,`h = 49 cm`
Let, `R` be radius of a base of a cone
The hemisphere is cast into the right circular cone,
Therefore,
Volume of hemisphere = Volume of cone
`2/3 pi r^3 = 1/3 pi R^2h `
`2 r^3 = R^2h`
`2 xx 7^3 = R^2 xx 49`
`2 xx 49 xx 7 = 49 R^2`
`R^2 = (2 xx 49 xx 7)/49`
`R^2 = 14`
`R = sqrt(14) `
`R = 3.74 cm`
Hence, the radius of a base of a cone is `3.74 cm`