Monica has a piece of Canvas whose area is 551 m² . She uses it to have a conical tent made, with a base radius of 7 m. Assuming that all the stitching margins and wastage incurred while cutting, amounts to approximately 1 m² . Find the volume of the tent that can be made with it.
Answers
Given : Area of canvas = 551 m²
Area of canvas wastage = 1 m²
Radius of a conical tent ,r = 7 m
Area of canvas used in making tent = (551 - 1) = 550 m²
Area of canvas used in making tent = 550 m²
∴ Surface area of a cone = πrl
πrl = 550
22/7 × 7 × l = 550
22 × l = 550
l = 550/22
l = 50/2
l = 25 m
Slant height, l = 25 m
Let 'h' be the height of the cone. Then,
l² = r² + h²
h² = l² - r²
h = √l² - r²
h = √25² - 7²
h = √625 - 49
h = √576
h = 24 m
Volume of the cone,V = ⅓ πr²h
V = ⅓ × 22/7 × 7 × 7 × 24
V = 22 × 7 × 8
V = 154 × 8
V = 1232 m³
Hence, the volume of the tent that can be made with it is 1232 m³.
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Answer:
Step-by-step
Given : Area of canvas = 551 m²
Area of canvas wastage = 1 m²
Radius of a conical tent ,r = 7 m
Area of canvas used in making tent = (551 - 1) = 550 m²
Area of canvas used in making tent = 550 m²
∴ Surface area of a cone = πrl
πrl = 550
22/7 × 7 × l = 550
22 × l = 550
l = 550/22
l = 50/2
l = 25 m
Slant height, l = 25 m
Let 'h' be the height of the cone. Then,
l² = r² + h²
h² = l² - r²
h = √l² - r²
h = √25² - 7²
h = √625 - 49
h = √576
h = 24 mVolume of the cone,V = ⅓ πr²h
V = ⅓ × 22/7 × 7 × 7 × 24
V = 22 × 7 × 8
V = 154 × 8
V = 1232 m³