Question

The vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel.

Answer 1

Hint: In this question remember that diameter of the cylinder is equal to the diameter of the hemisphere and also remember that height of the hemisphere is the radius of the hemisphere. The surface area of the hemisphere and cylinder is added to find the surface area of the vessel.

Complete step-by-step solution

According to the question,
A hollow hemisphere is mounted with a cylinder and radius of hemisphere = \[\dfrac{{14}}{2} = 7cm\]
And the total height of the system is 13cm, then we have to find the inner surface area of the system.
Now, we know that the total inner surface area = inner surface area of the hemisphere + Inner surface area of the cylinder.
Since, height of the cylinder = (height of the system – radius of hemisphere) = 13cm – 7cm = 6cm.
Therefore, total inner surface area = $2\pi {r^2} + 2\pi rh$
\[ \Rightarrow \]Total inner surface area $ = \left( {2 \times \dfrac{{22}}{7} \times {7^2} + 2 \times \dfrac{{22}}{7} \times 7 \times 6} \right)c{m^2}$
\[ \Rightarrow \]Total inner surface area$ = \left( {308 + 264} \right)c{m^2} = 572c{m^2}$
Therefore, the inner surface area of the vessel is equal to $572c{m^2}$

Note: To solve this type of questions, it is important to know the formulas of mensuration, like in this question we used the formulas:
Curved surface area of a hemisphere = $2\pi {r^2}$
Curved surface area of a cylinder = $2\pi rh$, where r is the radius, and h is the height of the cylinder.