Question

A vessel is 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

The radius(r) of the cylindrical part and the hemispherical part is the same (i.e., 7 cm)

Height of hemispherical part = Radius $=7$ cm
Height of cylindrical part (h) $=13-7=6$ cm

Inner surface are of the vessel = CSA of cylindrical part + CSA of hemispherical part
= $2\pi rh+2\pi r^2$

Inner surface area of vessel = $2\times \frac{22}{7}\times 7\times 6+2\times \frac{22}{7}\times 7\times 7$
= $44(6+7)$
= $44\times 13$
= $572c{m}^2$