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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.

Here r, the radius of hemisphere = 7 cm ,

h , the height of cylinder = (13 - 7) = 6 cm

Clearly, radius of the base of cylindrical part is also r cm

Surface area of the vessel = Curved surface area of the cylindrical part + Curved surface area of hemispherical part

$$= \ 2 \pi rh \ + \ 2 \pi r^2 \ = \ 2 \pi r(h \ + \ r)$$

$$= \ 2 \ × \ \frac{22}{7} \ × \ 7 \ × \ 13 \ = \ 572$$ cm2