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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
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.
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(use π = `22/7`)
