# 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]

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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