Question

The following figure represents a solid consisting of a right circular cylinder with a hemisphere at one end and a cone at the other. Their common radius is $7$cm. The height of the cylinder and cone are each of $4$cm. Find the volume of the solid.

Answer 1

The solid can be divided into $3$ parts.

The first part is the cone with height $4cm$ and radius $7cm$.

Volume of cone

$V_1=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\cdot \frac{22}{7}\cdot 7^2\cdot 4=205.34c{m}^3$

The second part is the cylinder with height $4cm$ and radius $7cm$.

Volume of cylinder

$V_2=\pi r^{2}h=\frac{22}{7}\cdot 7^2\cdot 4=616c{m}^3$

The third part is the hemisphere with radius $7cm$.

Volume of hemisphere

$V_3=\frac{2}{3}\pi r^3=\frac{2}{3}\cdot \frac{22}{7}\cdot 7^3=718.67c{m}^3$

Volume of total solid

$V_1+V_2+V_3=1540c{m}^3$