Question

A vessel is in the form of a hollow hemisphere surmounted 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.

Answer 1

Given diameter of the hemisphere = 14 cm

Radius of the hemisphere = 7 cm  `[∵ r = d/2]`

and total height = 13 cm

∴ Height of cylindrical portion = 13 − 7 = 6 cm

Curved surface area of cylindrical portion= 2πrh

= `2 xx 22/7 xx 7 xx 6`

= 2 × 22 × 6

= 264 cm²

Curved surface area of the hemispherical portion

= 2πr²

= `2 xx 22/7 xx (7)^2 ` 

= 2 × 22 × 7

= 308 cm²

∴ Total inner surface area = (264 + 308)

= 572 cm²

Hence, the inner surface area of the vessel is 572 cm².