# 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. - Mathematics

#### 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.

#### Solution

Let h be the height and r be the radius of the base of the conical tent.

According to the given information

77xx16 = 1/3 pir^2h

=> 77xx16=1/3 xx 22/7 xx7xx7xxh

=> 77xx 16 = 1/3 xx 22xx7 xx h

=> h = (77xx16xx3)/(22xx7) => h = 24m

Now, I^2 = r^2 + h^2

=> I^2= 7^2 + 24^2 = 625

=> I = 25

∴ Curved surface area = pirl = 22/7 xx 7 xx 25 = 550 m^2

Hence, the height of the tent is 24 m and the curved surface area of the tent is 550 m2

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