Q4 of 79 Page 244

A tent is in the shape of a right circular cylinder surmounted by a cone. The total height and the diameter of the base are 13.5 m and 28 m. If the height of the cylindrical portion is 3 m, find the total surface area of the tent.

Given, Total height = 13.5 m


Diameter of the base = 28 m


Height of the cylindrical portion = 3 m


Height of cone = 13.5-3


= 10.5 m


Radius of the base =


= 14 m


Lateral surface area of cylinder = 2rh


= 2143


= 84 m2


Lateral surface area of cone = rl ,


where l =


⇒ l =


⇒ l =


⇒ l =


⇒ l = 17.5


So, Lateral surface area of cone = 1417.5


= 245 m2


Total surface area = Lateral surface area of cylinder+ Lateral surface area of cone


Total surface area = 84 +245


= 329


= 329


= 1034 m2


Total surface area of the tent is 1034 m2.


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