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.