Question

A tent of height 77 dm is in the form of a right circular cylinder of diameter 36m and height 44 dm surmounted by a right circular cone. Find the cost of the canvas at Rs 3.50 per m².

Answer 1

Given: Height of the tent = 77dm

= 77/10 = 7.7m

The height of the conical portion = 44dm

= 44/10 = 4.4m

∴ The height of the cylindrical portion

= Height of the tent – Height of the conical portion

= 7.7 – 4.4

= 3.3m

Given Diameter of the cylinder, d = 36m

Radius = 36/2 = 18m

CSA of cylindrical portion = 2πrh

= 2 x 22/7 x 18 x 4.4

= 497.828

= 497.83 m² (approx.)

Firstly, we have to find the slant height (l) of the conical portion

⇒ l² = h² + r²

⇒ l² = (3.3)² + (18)²

⇒ l² = 10.89 + 324

⇒ l² = 334.89

⇒ l = √334.89

⇒ l = 18.3m

∴ CSA of the conical portion = πrl

= 22/7 x 18 x 18.3

= 1035.257

= 1035.26 m² (approx.)

So,

Total Surface Area of the tent = Surface area of conical portion + surface Area of cylindrical portion

= 1035.26 + 497.83

= 1533.09 m²

∴ Canvas required to make the tent = 1533.09 m²

Cost of 1m² canvas = Rs 3.50

Cost of 1533.09m² canvas = Rs 3.50 × 1533.09

= Rs 5365.815

= Rs 5365.82