Question

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

Answer 1

As per the parameters given in the question itself, we have

Diameter of the hemisphere, $d=14cm$

Radius of the hemisphere, $r=7cm[\because r=\frac{d}{2}]$

Height of cylindrical portion, $h=13–7=6cm$

Curved surface area of cylindrical portion can be calculated as follows:
$=2\pi rh=2\times \frac{22}{7}\times 7\times 6$ =$2\times 22\times 6$

$=264c{m}^2$

Curved surface area of hemispherical portion can be calculated as follows:
$=2\pi r^2$
$=2\times \frac{22}{7}\times 7^2$
$=308c{m}^2$

Total inner surface area $=308c{m}^2+264c{m}^2=572c{m}^2$

Hence, the inner surface area of the vessel is $572c{m}^2$.