Question

A hollow cylinder is surmounted on a hemispherical vessel. Diameter of hemisphere is 14 cm and total height of the vessel is 13 cm. Find the internal curved surface area of the vessel.

Answer 1

Given

Common diameter of cylinder and hemisphere = 14 cm

∴ Radius of hemisphere = \(\frac { 14 }{ 2 }\) = 7 cm

Radius of cylinder = 7 cm

∵ Total height of vessel = 13 cm

∴ Height of cylinder (h) = (13 – 7) = 6 cm

Internal curved surface area of vessel 

= Internal surface area of cylinder + internal surface area of hemisphere

= 2πrh + 2πr² = 2πr(h + r)

= 2 × \(\frac { 22 }{ 7 }\) × 7 × (6 + 7)

= 44 × 13 = 572 cm².

Hence, the total surface area of the vessel 

= 572 cm²