Question

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 its inner surface area.

Answer 1

Given:

Diameter of hemisphere = 14 cm

⇒ r = 7 cm

Total height of vessel = 13 cm

π = `22/7`

To Find: Inner surface area of the vessel

Step 1: Find the height of the cylindrical part

Total height = height of cylinder + radius of hemisphere

13 = h + 7

h = 13 − 7 = 6 cm

Step 2: Write the inner surface area formula

Inner surface area = curved surface area of hemisphere + curved surface area of cylinder

ISA = 2πr² + 2πrh

Step 3: Substitute values

(i) Curved surface area of a hemisphere

`2πr^2 = 2 × 22/7 xx 7^2`

= `2 xx 22/7 xx 49`

= 308 cm² 

(ii) Curved surface area of a cylinder

`2πrh = 2 × 22/7 xx 7 xx 6`

= 264 cm²

Step 4: Total inner surface area

ISA = 308 + 264

= 572 cm²