Question

A solid is in the form of a cone mounted on a right circular cylinder, both having same radii of their bases. Base of the cone is placed on the top base of the cylinder. If the radius of the base and height of the cone be $7$cm and $10$cm respectively, and the total height of the solid be $30$cm, find the volume of the solid.

Answer 1

Cylindrical part: $r=7cm,h=30-10=20cm$
Conical part: $r=7cm,h=10cm$
Volume of the solid$=$ Volume of cylinder$+$ Volume of cone
$=\pi r^{2}h+\frac{1}{3}\pi r^{2}h$
$=\frac{22}{7}\times 7\times 7\times 20c{m}^2+\frac{1}{3}\times \frac{22}{7}\times 7\times 7\times 10$
$=3080c{m}^3+\frac{1540}{3}c{m}^3$
$=3080+513.33c{m}^3$
Volume of the solid$=3593.33c{m}^3$.