Q6 of 44 Page 14

A tent of height 77 dm is in the form of a right circular cylinder of diameter 36m and height 44 dm surmounted by a right circular cone. Find the cost of the canvas at Rs 3.50 per m2.


Given: Height of the tent = 77dm



The height of the conical portion = 44dm



∴ The height of the cylindrical portion


= Height of the tent – Height of the conical portion


= 7.7 – 4.4


= 3.3m


Given Diameter of the cylinder, d = 36m



CSA of cylindrical portion = 2πrh



= 497.828


= 497.83 m2 (approx.)


Firstly, we have to find the slant height (l) of the conical portion


⇒ l2 = h2 + r2


⇒ l2 = (3.3)2 + (18)2


⇒ l2 = 10.89 + 324


⇒ l2 = 334.89


⇒ l = √334.89


⇒ l = 18.3m


∴ CSA of the conical portion = πrl



= 1035.257


= 1035.26 m2 (approx.)


So,


Total Surface Area of the tent = Surface area of conical portion + surface Area of cylindrical portion


= 1035.26 + 497.83


= 1533.09 m2


∴ Canvas required to make the tent = 1533.09 m2


Cost of 1m2 canvas = Rs 3.50


Cost of 1533.09m2 canvas = Rs 3.50 × 1533.09


= Rs 5365.815


= Rs 5365.82


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