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 the inner surface area and the volume of the vessel.

Answer 1

Given diameter hemisphere d = 14 cm

`r = d/2 = 14/2`

r = 7 cm

Height of cylinder h = 6 cm

Total inner surface Area of vessel

= CSA of cylinder + CSA of hemisphere

= 2πrh + 2πr² 

= 2πr (h + r)

= `2 xx 22/7 xx 7 (6 + 7)`

= 44 × 13

= 572 cm²

Now, the Volume of the vessel

= `pir^2h + 2/3pir^3`

= `pir^2(h + 2/3r)`

= `22/7 xx (7)^2 (6 + 2/3 xx 7)`

= `154 xx 32/3`

= 1642.67 cm³