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Question
A conical tent is 10 m high and the radius of its base is 24 m. Find
- slant height of the tent.
- cost of the canvas required to make the tent, if the cost of 1 m2 canvas is ₹ 70.
`["Assume "pi=22/7]`
Solution
(i) Let ABC be a conical tent.
Height (h) of conical tent = 10 m
Radius (r) of conical tent = 24 m
Let the slant height of the tent be l.
In ΔABO,
AB2 = AO2 + BO2
l2 = h2 + r2
= (10 m)2 + (24 m)2
= 676 m2
∴ l = 26 m
Therefore, the slant height of the tent is 26 m.
(ii) Curved surface area of the tent = πrl
= `(22/7xx24xx26)m^2`
= `13728/7 m^2`
Cost of 1 m2 canvas = ₹ 70
`"Cost of "13728/7 m^2 " canvas"` = `₹ (13728/7xx70)`
= ₹ 137280
Therefore, the cost of the canvas required to make such a tent is ₹ 137280.
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