A man uses a piece of canvas having an area of 551 m , to make conical tent of Base radius 7m .Assuming that all the stitching margin and wastage incurred while cutting the amount to approximately 1 m find the volume of the tent that can be made with it
Answers
Given : A man uses a piece of canvas having an area of 551 m² , to make conical tent of Base radius 7m
stitching margin and wastage incurred while cutting the amount to approximately 1 m²
To Find : volume of the tent that can be made with it
Solution:
canvas having an area of 551 m²
wastage = 1 m²
cloth Area = 551 - 1 = 550 m²
Case1 : Assuming no Base of Tent
Surface Area of tent = πRL = 550
R = 7 m , h = height L = slant height
=> L = 550/ πR
=> L = 550/ (22/7)7
=> L = 25 m
L² = R² + h²
=> 25² = 7² + h²
=> h = 24
Volume = (1/3) πR²h
= (1/3) (22/7)7²(24)
= 1232 m³
Case2 : Assuming Base of Tent
Surface Area of tent = πR² + πRL = 550
R = 7 m , h = height L = slant height
=> L = (550 - 154)/ πR
=> L = 396/ (22/7)7
=> L = 18 m
L² = R² + h²
=> 18² = 7² + h²
=> h = 5√11 = 16.58 m
Volume = (1/3) πR²h
= (1/3) (22/7)7²(16.58)
= 851.1 m³
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