A hollow spherical shell is made of a metal of density 4.5 g per cm3.

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.

Solution:

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

Volume of the shell $=\frac{4}{3} \pi\left(R^{3}-r^{3}\right)$

$=\frac{4}{3} \pi\left(9^{3}-8^{3}\right)$

$=\frac{4}{3} \times \frac{22}{7} \times(729-512)$

$=\frac{4 \times 22 \times 217}{21}$

$=\frac{88 \times 31}{3}$

$=\frac{2728}{3} \mathrm{~cm}^{3}$

Weight of the shell = volume of the shell $\times$ density per cubic $\mathrm{cm}$

$=\frac{2728}{3} \times 4.5 \approx 4092 \mathrm{~g}=4.092 \mathrm{~kg}$