A full ice cream cone with a radius of $5 \mathrm{cm}$and a height of $10 \mathrm{cm}$as shown. Calculate the volume of ice cream (to the nearest integer, in ${\mathrm{cm}}^3$) assuming that the $\frac{1}{6}$th part remains empty.

Given solid is a combination of cone and hemisphere Because the volume of a hemisphere is half that of a sphere, it is written as the Volume of hemisphere $\frac{2}{3}\pi R^3$, where r is the radius of the hemisphere.

The volume of the cone is $\frac{1}{3}\pi R^{2}h$

The volume of ice cream =Volume of hemisphere + Volume of a cone

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

The radius of the hemisphere =Radius of the cone

Since the height of the hemisphere is $5 \mathrm{cm}$, then the height of the cone will be $5 \mathrm{cm}$

 The volume of ice cream

$=\frac{2}{3}\pi (5{)}^3+\frac{1}{3}\pi (5{)}^2\times 5$

$=125\pi =392.85$

$\frac{1}{6}$ th of ice cream $=\frac{392.85}{6}=65.475$

The volume of required portion of ice cream $=392.85-65.47=327.375{ \mathrm{cm}}^3$