Question

A conical tent is to accommodate 77 persons. Each person must have 16 m³ of air to breathe. Given the radius of the tent as 7 m, find the height of the tent and also its curved surface area. 

Answer 1

According to the condition in the question, 

`77 xx 16 = 1/3 pir^2h`

`=> 77 xx 16 = 1/3 xx 22/7 xx 7 xx 7 xx h`

`=> h = (77 xx 16 xx 3 xx 7)/(22 xx 7 xx 7)`

`=> h = (11 xx 16 xx 3)/22`

`=>` h = 24 m

We know that,

l² = r² + h²

`=>` l² = (7)² + (24)²

`=>` l² = 49 + 576

`=>` l² = 625

`=>` l = 25 m

∴ Curved Surface Area = πrl

= `22/7 xx 7 xx 25`

= 550 m²

Therefore the height of the tent is 24 m and it curved surface area is 550 m².