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Question
A conical tent with a capacity of 600 m3 stands on a circular base of area 160 m2 Find in m2 the area of the canvas.
Solution
Area of the circular base = 160m2
`pir^2 = 160`
⇒ `r = sqrt((160 xx 7)/22)`
⇒ `r = sqrt(50.909)` = 7.134 m
Therefore , radius = 7.134 m
Capacity or Volume of the tent = 600m3
`1/3pir^2h = 600`
⇒ `1/3 xx 22/7 xx 7.13 xx 7.13 xx h = 600`
⇒ `h = (600 xx 3 xx 7)/(7.13 xx 7.13 xx 22)`
⇒ h = 11.265m
Therefore , vertical height = 11.265 m
We know slant height (l) =
l = `sqrt(r^2 + h^2)`
⇒ `l = sqrt(7.134^2 + 11.265^2)`
⇒ `l = sqrt(177.624) = 13.327`
Therefore , slant height = 13.327 m
The curved surface area = `pirl = 22/7 xx 7.134 xx 13.327` = 298.9m2
Hence , the area of the canvas = 298.9 m2
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