A solid wooden toy is in the shape of a right circular cone mounted on a hemisphere. If the radius of the hemisphere is 4.2 cm and the total height of the toy is 10.2 cm, find the volume of the wooden toy.

Explanation

Volume of the toy = Volume of the hemispherical part + Volume of conical part
Volume of a hemisphere of radius` ('r') =2/3 pir^3`
Volume of a cone `=1/3 pir^2h`
where `r`is the radius of the base of the cone and h is the height.
The hemisphere and the cone will have the same radius` r =4.2cm`
Since total length of the toy is `10.2 cm`
the length of the conical part will be `10.2−4.2=6cm`
Hence, Volume of the solid` =(2/3xx22/7xx4.2^3)+(1/3xx22/7xx4.2^2xx6)`
`=266.112cm^3`