A solid toy is in the form of a hemisphere surmounted by a right circular cone. height of the cone is 2 cm and the diameter of the base is 4 cm. If a right circular cylinder circumscribes the toy, find how much more space it will cover.
We have to find the remaining volume of the cylinder when the toy is inserted into it. The toy is a hemisphere surmounted by a cone.
Radius of cone, cylinder and hemisphere $(r)=2 \mathrm{~cm}$
Height of $\operatorname{cone}(l)=2 \mathrm{~cm}$
Height of the cylinder $(h)=4 \mathrm{~cm}$
So the remaining volume of the cylinder when the toy is inserted into it,
$=\pi r^{2} h-\left(\frac{1}{3} \pi r^{2} l+\frac{2}{3} \pi r^{3}\right)$
Put the values to get,
$=16 \pi-\left(\frac{8 \pi}{3}+\frac{16 \pi}{3}\right)$
$=16 \pi-8 \pi$
$=8 \pi$