Q7 of 44 Page 14

A tent of height 3.3 m is in the form of a right circular cylinder of diameter 12m and height 2.2m, surmounted by a right circular cone of the same diameter. Find the cost of the canvas of the tent at the rate of Rs. 500 per m2.


Given: Height of the tent = 3.3 m


The height of the cylindrical portion = 2.2 m


∴ The height of the conical portion


= Height of the tent – Height of the cylindrical portion


= 3.3 – 2.2


= 1.1m


Given Diameter of the cylinder, d = 12m



CSA of cylindrical portion = 2πrh



= 82.971 m2


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


⇒ l2 = h2 + r2


⇒ l2 = (1.1)2 + (6)2


⇒ l2 = 1.21 + 36


⇒ l2 = 37.21


⇒ l = √37.21


⇒ l = 6.1m


∴ CSA of the conical portion = πrl



= 115.029 m2


So,


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


= 115.029 + 82.971


= 198 m2


∴ Canvas required to make the tent = 198 m2


Cost of 1m2 canvas = Rs 500


Cost of 198 m2 canvas = Rs 500 × 198


= Rs 99000


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