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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
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 = 24`m
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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