Question

A 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( in $c{m}^2$).

Answer 1

It is given that diameter of hemisphere = 14 $cm$

Therefore, radius of hemisphere $\left(r\right)=\frac{14}{2}=7cm$

Radius of hemisphere= radius of cylinder = $r$ =7 $cm$

Height of Cylinder = [Height of Vessel] - [Radius of Hemisphere]
$\Rightarrow$ $h$ = 13-7 = 6 $cm$
Inner Surface Area of Vessel = Inner Surface area of Cylinder + Inner Surface Area of Hemisphere
$=2\pi rh+2\pi r^2=(2\times \frac{22}{7}\times 7\times 6)+2\times \frac{22}{7}\times 7\times 7$
$=264+308=572c{m}^2$