A tent of height 77 dm is in the form of a right circular cylinder of diameter 36 m and height 44 dm surmounted by a right circular cone. Find the cost of the canvas at Rs. 3.50 per m2 .
Given: height of the tent, H = 77dm = 7.7 m
Height of the cylindrical portion, h = 44dm = 4.4m
∴ Height of the conical portion, h’ = 7.7 – 4.4 = 3.3 m
Radius of the cylinder, r = 36/2 = 18m
Curved surface area of the cylindrical portion of the tent = 2 π r2 h
= 2 × π × (18)2 × 4.4
= 158.4 π m2
Slant height of the conical portion of the tent =
= 18.3 m
∴ Curved surface area of the conical portion = π × 18 × 18.3
= 329.4 π m2
∴ Total surface area of the tent = 158.4 π + 329.4 π
= 487.8 π
= 1533.09 m2
∴ Canvas required to make the tent = 1533.09 m2
Total cost of the canvas = 1533.09 × 3.50
= Rs5365.80