A circus tent is to be erected in the form of a cone surmounted on a cylinder. The total height of the tent is 49m, diameter of the base is 42m and the height of the cylinder is 21m. Find the cost of canvas needed to make e tent, if the cost of canvas is Rs.12.50 per m^2
Answers
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The cost of canvas needed to make e tent is Rs. 63,525.
Given:
Total height of tent =49m
Radius of base(r) = diameter/2 = 42/2 = 21m
Height of cylinder(h) = 21m
Cost of canvas = 12.50m²
To find:
Cost of canvas needed to make tent
Solution:
For finding out the cost of canvas, total surface area of tent is neede.
Since tent is made of cone and cylinder,
Total surface area of tent = Curved surface area of cone + Curved surface area of cylinder.
Curved surface area of cylinder = 2πrh
= 2*21*(22/7)*21
= 2772m².
Height of cone(h) = height of tent - height of cylinder = 49-21 = 28m
Radius of cone(r) = radius of cylinder = 21m.
Slant height of cone(l) = √r² + h²
= √21²+28²
= √441 + 784 = √1225
= 35m.
Curved surface area of cone = πrl
= (22/7) * 21*35
= 2310m².
Total surface area of tent = Curved surface area of cone + Curved surface area of cylinder.
= 2772 + 2310
= 5082m²
The total cost of the canvas = Rs. 12.50/m²×5082m²
The total cost of the canvas = Rs. 63,525
Hence, the cost of canvas needed to make e tent is Rs. 63,525.
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