Question

A hollow spherical shell is made of a metal of density 4.5 g per cm³. If its internal and external radii are 8 cm and 9 cm respectively, find the weight of the shell.

Answer 1

Internal radius of the hollow spherical shell, r= 8 cm
External radius of the hollow spherical shell, R= 9 cm

Volume of the shell = $\frac{4}{3}\mathrm{\pi }\left(R^3-r^3\right)$
$$\begin{gathered} =\frac{4}{3}\mathrm{\pi }\left(9^3-8^3\right) \\ =\frac{4}{3}\times \frac{22}{7}\times \left(729-512\right) \\ =\frac{4\times 22\times 217}{21} \\ =\frac{88\times 31}{3} \\ =\frac{2728}{3}{\mathrm{cm}}^3 \end{gathered}$$

Weight of the shell = volume of the shell $\times$ density per cubic cm
= $\frac{2728}{3}\times 4.5\approx 4092\mathrm{g}=4.092\mathrm{kg}$

∴ Weight of the shell = 4.092 kg