Question

A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The radius of the hemisphere is 7 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel.

Answer 1

Hint: surface area of hemisphere of radius r is given by ${S_1} = 2\pi {r^2}$ . Surface area of curved surface of a cylinder of radius r and height h is ${S_2} = 2\pi rh$ .

Complete step-by-step answer:

We have given that, radius of the hemisphere and cylinder is $r = 7cm$and height if the cylinder is $h = 13cm$. We know that, surface area of the hemisphere of radius r is given by ${S_1} = 2\pi {r^2}$ . Surface area of curved surface of a cylinder of radius r and height h is ${S_2} = 2\pi rh$. Hence the total surface area is,
$\begin{gathered}
  S = 2\pi {r^2} + 2\pi rh \\
   \Rightarrow S = 2\pi \times {7^2} + 2\pi \times 7 \times 13 \\
   \Rightarrow S = 280\pi c{m^2} \\
\end{gathered} $

Note: In order to solve mensuration problems, one has to make use of the appropriate formulas needed to solve the problem