The internal and external diameters of a hollow hemispherical vessel are $14 \; cm$ and $21 \; cm$ respectively. Find the total surface area of the vessel. Take $\pi = \dfrac{22}{7}$
Given: $\;$ Internal diameter of the vessel $= 14 \; cm$;
External diameter of the vessel $= 21 \; cm$
$\therefore \;$ Internal radius of the hemispherical vessel $= r = 7 \; cm$
External radius of the hemispherical vessel $= R = 10.5 \; cm$
Total surface area of the hemispherical vessel (T.S.A) $= $ External surface area $+$ Internal surface area $+$ Area of the ring
$\begin{aligned}
i.e. \; T.S.A & = 2 \pi R^2 + 2 \pi r^2 + \pi \left(R^2 - r^2\right) \\\\
& = 2 \pi \left(R^2 + r^2\right) + \pi \left(R^2 - r^2\right) \\\\
& = 2 \pi \left(10.5^2 + 7^2\right) + \pi \left(10.5^2 - 7^2\right) \\\\
& = 318.5 \pi + 61.25 \pi \\\\
& = 379.75 \pi = 379.75 \times \dfrac{22}{7} = 1193.5 \; cm^2
\end{aligned}$