Question

A conical tent has the area of base 154 m² and its curved surface area is 550 m², find the volume of the tent.

Answer 1

Take π = 22/7

Base area: πr² = 154 

⇒ `(22/7) r^2`

= 154

⇒ r² = 49

⇒ r = 7 m

Curved surface: `π r l = 550`

⇒ `(22/7)·7·l`

= `550

⇒ l = 25 m

Height: h = `sqrt(l^2 − r^2)`

= `sqrt(25^2 − 7^2)`

= `sqrt(625 − 49)`

= `sqrt576`

= 24 m

Volume: V = `(1/3) π r^2 h`

= `(1/3)·(22/7)·7^2·24`

= 1232 m³