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Question
A tent of height 77dm is in the form a right circular cylinder of diameter 36m and height 44dm surmounted by a right circular cone. Find the cost of canvas at Rs.3.50 per m2 ?
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Solution
Given that height of a tent = 77dm
Height of cone = 44dm
Height of a tent without cone = 77 - 44 = 33dm
= 3.3m
Given diameter of cylinder (d) = 36m
Radius (r) = `36/2`= 18m
Let ‘l’ be slant height of cone
`l^2=r^2+h^2`
`l^2=18^2+3.3^2`
l2 = 324 + 10.89
l2 = 334.89
l = 18.3
Slant height of cone l = 18.3
Curved surface area of cylinder (S1) = 2πrh
= 2 x π x18 x 4.4m2 ............(1)
Curved surface area of cone (S2) = πrl
= π18 x 18.3m2 .............(2)
Total curved surface of tent = S1 + S2
T.C.S.A = S1 + S2
= 1532.46m2
Given cost canvas per m2 = RS 3.50
Total cost of canvas per 1532.46 X 3.50
= 1532.46 X 3.50
= 5363.61
∴ Total cost of canvas = Rs 5363.61
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