Question

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( use π = \(\frac{22}7\)).

Answer 1

Given: 

height of the tent, H = 77 dm = 7.7 m 

Height of the cylindrical portion, h = 44 dm = 4.4 m 

∴ Height of the conical portion, h’ = 7.7 – 4.4 = 3.3 m 

Radius of the cylinder, r = \(\frac{36}2\) = 18 m 

Curved surface area of the cylindrical portion of the tent 

= 2πr² h 

= 2 × π × (18)² × 4.4 

= 158.4 π m² 

Slant height of the conical portion of the tent = \(\sqrt{3.3^2 + 18^2}\)

= 18.3 m 

∴ Curved surface area of the conical portion = π × 18 × 18.3 

= 329.4π 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 

= Rs 5365.80