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Question
The circumference of the base of a 10 m high conical tent is 44 metres. Calculate the length of canvas used in making the tent if the width of the canvas is 2m. (Take π = 22/7)
Solution
Let r m be the radius of the base, h m be the height and l m be the slant height of the cone. Then,
Circumference = 44 metres
⇒ 2πr = 44
⇒ 2 x `22/7` x r = 44
⇒ r = 7 metres
It is given that h = 10 metres
∴ l2 = r2 + h2
⇒ l = `sqrt( r^2 + h^2)`
l = `sqrt(49 + 100) = sqrt(149) = 12.2 "m"`
Now, Surface area of the tent = πrl m2
= `22/7 xx 7 xx 12.2` m2
= 268.4 m2
∴ Area of the canvas used = 268.4 m2
It is given that the width of the canvas is 2 m.
∴ Length of the canvas used = `"Area"/"Width"`
= `268.4/2`
= 134.2 metres
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