Question

A tent of height 77 dm is in the form 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

Height of tent = 77dm 

= 7.7m  

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

Height of cylinder = 44dm = 4.4m 

Height of cone = (7.7- 4.4) m 

= 3.3m 

Curved Surface area of cylinder portion of the tent = 2π x r x h

= 2 × (\(\frac{22}7\)) × 18 × 4.4 

= 497.83 m² 

Curved surface area of conical tent =π r l 

Slant height of cone = \(\sqrt{(3.3^2 + {18}^2)}\)

18.3m 

Curved surface area of cone = (22/7) × 18 × 18.3 

= 1035.26m² 

Total surface area of the tent = 497.83m² + 1035.26m² = 1533.09m² 

Total cost of canvas = 3.50 × 1533.09 

= Rs 5365.82