Question

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

Answer 1

Step-by-step explanation:

answer is 1232..........

Answer 2

Given,

Tent is conical

The number of person tent can accommodate 77

Air to breath = 16m³

The radius of the conical tent r =7m

To Find,

Height and curved surface area of the tent.

Solution,

The air needed by each person =16m³

Total air needed for 77 people =

77 × 16 =1232m³

Total air in a tent means its volume.

Therefore,

The volume of the  tent = total air in the tent

$\frac{1}{3}$$\pi r^{2} h$ = 1232

r = 7m

$\frac{1}{3}\pi *7^{2}*h$  = 1232

$\frac{1}{3}$×$\frac{22}{7}$×7×7×h = 1232

$\frac{22*7}{3}$ = $\frac{154}{3}$

51 h =1232

h = 1232/ 51

  = 24m

Curved surface area = $\pi$×r×l

             =  3.14*7*l

l ² = h²+r²      

l =√h²+r ²

=√24²+7²    

= √576+49

=√625

=25m

Therefore,

surface are = 3.14×7×25

             = 549.5 m²    

The height of the tent is 24m and the surface area is 549.5m²