Question

A right triangle with sides 6 cm, 8 cm and 10 cm is revolved about the side 8 cm. find the volume and the curved surface area of the solid so formed.

Answer 1

When a right triangle with sides 6 cm, 8 cm and 10 cm is revolved about the side 8 cm, then solid formed is a cone whose height, h = 8 cm.
The radius of the cone, r = 6 cm.
Slant height of the cone, l = 10 cm

$\therefore$ Volume of the cone
$=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\times \frac{22}{7}\times 6\times 6\times 8$
$=\frac{6336}{21}=301.7c{m}^3$

Curved surface area of the cone $=\pi rl$
$=\frac{22}{7}\times 6\times 10=\frac{1320}{7}=188.5c{m}^2$

Hence, the volume and surface area of the cone are $301.7c{m}^3$ and $188.5c{m}^2$ respectively.