Question:
The outer diameter of a spherical shell is 12 cm and its inner diameter is 8 cm. Find the volume of metal contained in the shell. Also, find its outer surface area.
Solution:
Outer radius of the spherical shell = 6 cm
Inner radius of the spherical shell = 4 cm
Volume of metal contained in the shell $=\frac{4}{3} \times \frac{22}{7}\left(6^{3}-4^{3}\right)$
$=\frac{88}{21} \times(216-64)$
$=\frac{88}{21} \times 152$
$=636.95 \mathrm{~cm}^{3}$
$\therefore$ Outer surface area $=4 \times \frac{22}{7} \times 6 \times 6$
$=452.57 \mathrm{~cm}^{2}$