Q. 95.0( 3 Votes )

A tent is made in the form of a conic frustum, surmounted by a cone. The diameters of the base and top of the frustum are 14m and 7 m and its height is 8 m. The height of the tent is 12m. Find the quantity of canvas required. [Take π=22/7]

Answer :


For the lower portion of the tent:


Diameter of the base = 14 m


Radius, R, of the base = 7 m


Diameter of the top end of the frustum = 7 m


Radius of the top end of the frustum =


Height of the frustum = h = 8 m


Slant height = l = √{h2 + (R – r)2}


= √{(8)2 +(7 – 3.5)2


= √64 + (3.5)2


= √64 + 12.25


= √76.25


= 8.73 m


For the conical part


Radius of the cone base = r = 3.5 m


Height of the cone = Height of the tent – height of frustum


= 12 – 8


= 4 m


Slant height of cone = L = √(4)2+(3.5)2


= √16 + 12.25


=√28.25


= 5.3 m


Total quantity of canvas = CSA of frustum + CSA of conical top


= πl(R + r) + πrL


= π [8.73(7 + 3.5) + 3.5 × 5.3]




= 346.5 m2


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