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 cone` h=49 cm`
Volume of hemisphere `V=2/3pir^3`
`=2/3pixx7^3cm^3`
`=2/3xx343xxpicm^3`
`=686/3picm^3`
Volume of cone `V=1/3pir^2h`
`=1/3pir^2xx49cm`
The hemisphere is cast into a right circular cone of hight `(h=49 cm)` and have base radius `r`.
Volume of hemisphere = Volume of cone
`686/3picm^3=1/3pir^2xx49cm`
`r^2=686/49 cm^2`
`r^2=14cm^2`
`r=sqrt14`
Hence, radius of base of cone `r=3.74 cm`