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.

Answer 1

Outer radius of the spherical shell = 6 cm
Inner radius of the spherical shell = 4 cm

$$\begin{gathered} \mathrm{Volume}\mathrm{of}\mathrm{metal}\mathrm{contained}\mathrm{in}\mathrm{the}\mathrm{shell}=\frac{4}{3}\times \frac{22}{7}\left(6^3-4^3\right) \\ =\frac{88}{21}\times \left(216-64\right) \\ =\frac{88}{21}\times 152 \\ =636.95{\mathrm{cm}}^3 \end{gathered}$$


$$\begin{gathered} \therefore \mathrm{Outer}\mathrm{surface}\mathrm{area}=4\times \frac{22}{7}\times 6\times 6 \\ =452.57{\mathrm{cm}}^2 \end{gathered}$$