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Question
A tent is in the shape of a cylinder surmounted by a conical top. If the height and radius of the cylindrical part are 3 m and 14 m respectively, and the total height of the tent is 13.5 m, find the area of the canvas required for making the tent, keeping a provision of 26 m2 of canvas for stitching and wastage. Also, find the cost of the canvas to be purchased at the rate of ₹ 500 per m2.
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Solution
Radius of the cylindrical tent (r) = 14 m
Total height of the tent = 13.5 m
Height of the cylinder = 3 m
Height of the conical part = 10.5 m
Slant height of the cone (l) = `sqrt(h^2 + r^2)`
= `sqrt((10.5)^2 + (14)^2`
= `sqrt(110.25 + 196)`
= `sqrt(306.25)`
= 17.5 m
Curved surface area of cylindrical portion
= 2πrh
= `2 xx 22/7 xx 14 xx 3`
= 264 m2
Curved surface area of conical portion
= πrl
= `22/7 xx 14 xx 17.5`
= 770 m2
Total curved surface area = 264 m2 + 770 m2 = 1034 m2
Provision for stitching and wastage = 26 m2
Area of canvas to be purchased = 1060 m2
Cost of canvas = Rate × Surface area
= 500 × 1060
= ₹ 5,30,000/-
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