Question

A hemi-spherical tank is made up of an iron sheet $1cm$ thick. If the inner radius is$1m$, then find the volume of the iron used to make the tank. (Assume $\mathrm{\pi }=\frac{22}{7}$)

Answer 1

Inner Radius of the tank, (r) $=1m$

The thickness of the hemispherical tank $=1cm=0.01m$

Therefore, the outer Radius (R) $=1+0.01=1.01m$

Volume of the iron used in the hemi-spherical tank

$$\begin{gathered} =\frac{2}{3}\mathrm{\pi }\left({\mathrm{R}}^3-{\mathrm{r}}^3\right) \\ =\frac{2}{3}\times \frac{22}{7}\times \left(1.{01}^3-1^3\right) \\ =0.06348{\mathrm{m}}^3 \end{gathered}$$

Hence, the volume of the iron used in the hemispherical tank is $0.06348m^3$