Question

A hemispherical tank is made up of an iron sheet 1 cm thick. If the inner radius is 1m, then find the volume of the iron used to make the tank.

Answer 1

Inner radius (r1) of hemispherical tank = 1 m
Thickness of iron = 1cm = $\frac{1}{100}$ m = 0.01 m
Outer radius of the tank, R = 1 m + 0.01m = 1.01m

Volume of the iron used to make the tank = $\frac{2}{3}\pi$ R3 - $\frac{2}{3}\pi$ r3
$= \frac{2}{3}\pi$ (R3 - r3)

$= \frac{2}{3} × \frac{22}{7} ×$ [(1.01m)3 - (1m)3]

$= \frac{2}{3} × \frac{22}{7} ×$ [1.030301 m3 - 1 m3]

$= \frac{2}{3} × \frac{22}{7}$ $×$ 0.030301 m3
= 0.06348 m3 (approx.)

Therefore, 0.06348 m3 of iron is used to make the tank.