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