# 2. 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.

Since the vessel consists of hemisphere and cylinder, thus its area is given by :

Area of vessel   =  Inner area of the cylinder(curved)  +  Inner area of hemisphere

The inner surface area of the hemisphere is :

$=\ 2\pi r^2$

or                                            $=\ 2\times \left ( \frac{22}{7} \right ) \times 7^2$

or                                           $=\ 308\ cm^2$

And the surface area of the cylinder is  :

$=\ 2\pi rh$

or                                           $=\ 2\times \frac{22}{7}\times 7\times 6$

or                                           $=\ 264\ cm^2$

Thus the inner surface area of the vessel is  $= 308 + 264 = 572 \:cm^2.$

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