Question

A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone is $2cm$ and the diameter of the base is $4cm$. Determine the volume of the toy. If a right circular cylinder circumscribes the toy, find the difference of the volume of the cylinder and toy. (Take $\pi =3.14)$.

Answer 1

Volume of the toy

$=\frac{1}{3}\pi r^{2}h+\frac{2}{3}\pi r^3$

$=\frac{1}{3}\pi \times 2^2\times 2+\frac{2}{3}\pi \times 2^3$

$=25.12c{m}^3$

Volume of the cylinder circumscribing

$h=4cm$

$r=2cm$

$v=\pi r^{2}h=\pi \times 4\times 4=50.24c{m}^3$

Difference in volume$=(50.24-25.12)c{m}^3=25.12c{m}^3$