Q31 of 47 Page 1

A tent consists of a frustum of a cone, surmounted by a cone. If the diameter of the upper and lower circular ends of the frustum be 14 m and 26 m respectively, the height of the frustum be 8 m and the slant height of the surmounted conical portion be 12 m, find the area of canvas required to make the tent. (Assume that the radii of the upper circular end of the frustum and the base of surmounted conical portion are equal).

Given, Upper radius of the frustum = Radius of the surmounted cone = R = = 7 m

Lower radius of the frustum = r = = 13 m


Height of the frustum = h1 = 8 m


Slant height of the surmounted cone = l2 = 12 m


Slant height of the frustum =




⸫ l1 = 10 m


Lateral surface area of a cone = πRl2


Lateral surface area of a frustum = π (R + r) l1


Area of canvas required = Lateral area of cone + Lateral area of frustum


= ( × 7 × 12) + ( × (7 + 13) × 10)


= (84 + 200)


= 892.57 m2


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