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प्रश्न
A circus tent is cylindrical to a height of 8 m surmounted by a conical part. If total height of the tent is 13 m and the diameter of its base is 24 m; calculate :
- total surface area of the tent,
- area of canvas, required to make this tent allowing 10% of the canvas used for folds and stitching.
उत्तर
Height of the cylindrical part = H = 8 m
Height of the conical part = h = (13 – 8) m = 5 m
Diameter = 24 m ⟶ radius = r = 12 m
Slant height of the cone = l
`l = sqrt(r^2 + h^2)`
`l = sqrt(12^2 + 5^2)`
`l = sqrt(169) = 13 m`
Slant height of cone = 13 m
i. Total surface are of the tent
= 2πrh + πrl
= πr(2h + l)
= `22/7 xx 12 xx (2 xx 8 + 13)`
= `264/7(16 + 13)`
= `264/7 xx 29`
= `7656/7 m^2`
= 1093.71 m2
ii. Area of canvas used in stitching = Total area
Total area of canvas = `7656/7 + "Total area of canvas"/10`
`=>` Total area of canvas – `"Total area of canvas"/10 = 7656/7`
`=> "Total area of canvas" (1 - 1/10) = 7656/7`
`=> "Total area of canvas" xx 9/10 = 7656/7`
`=>` Total area of canvas = `7656/7 xx 10/9`
`=>` Total area of canvas = `76560/63 = 1215.23 m^2`
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