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How many meters of cloth of 5 m width will be required to make a conical tent. The radius of whose base is 7 m and heights is 24 m?
- a)120 m
- b)110 m
- c)125 m
- d)130 m
Correct answer is option 'B'. Can you explain this answer?
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How many meters of cloth of 5 m width will be required to make a conic...
To determine the amount of cloth required to make a conical tent, we need to calculate the curved surface area of the cone.
The formula to calculate the curved surface area of a cone is given by:
Curved Surface Area = π * r * l
where r is the radius of the base and l is the slant height of the cone.
1. Calculate the slant height of the cone:
Using the Pythagorean theorem, we can find the slant height (l) of the cone.
The height (h) of the cone is given as 24 m and the radius (r) is given as 7 m.
Using the Pythagorean theorem, we have:
l^2 = r^2 + h^2
l^2 = 7^2 + 24^2
l^2 = 49 + 576
l^2 = 625
l = √625
l = 25 m
2. Calculate the curved surface area of the cone:
Curved Surface Area = π * r * l
Curved Surface Area = π * 7 * 25
Curved Surface Area = 175π
3. Calculate the length of cloth required:
The width of the cloth is given as 5 m. To find the length required, we divide the curved surface area by the width.
Length of cloth required = Curved Surface Area / Width
Length of cloth required = (175π) / 5
Length of cloth required = 35π
Approximating π as 3.14, we can calculate the value:
Length of cloth required ≈ 35 * 3.14
Length of cloth required ≈ 109.9 m
Therefore, the correct answer is option (B) 110 m.
The formula to calculate the curved surface area of a cone is given by:
Curved Surface Area = π * r * l
where r is the radius of the base and l is the slant height of the cone.
1. Calculate the slant height of the cone:
Using the Pythagorean theorem, we can find the slant height (l) of the cone.
The height (h) of the cone is given as 24 m and the radius (r) is given as 7 m.
Using the Pythagorean theorem, we have:
l^2 = r^2 + h^2
l^2 = 7^2 + 24^2
l^2 = 49 + 576
l^2 = 625
l = √625
l = 25 m
2. Calculate the curved surface area of the cone:
Curved Surface Area = π * r * l
Curved Surface Area = π * 7 * 25
Curved Surface Area = 175π
3. Calculate the length of cloth required:
The width of the cloth is given as 5 m. To find the length required, we divide the curved surface area by the width.
Length of cloth required = Curved Surface Area / Width
Length of cloth required = (175π) / 5
Length of cloth required = 35π
Approximating π as 3.14, we can calculate the value:
Length of cloth required ≈ 35 * 3.14
Length of cloth required ≈ 109.9 m
Therefore, the correct answer is option (B) 110 m.
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Community Answer
How many meters of cloth of 5 m width will be required to make a conic...
Curved surface = πrl = 22/7 × 7 × 25 = 550 m2
Length of canvas used
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How many meters of cloth of 5 m width will be required to make a conical tent. The radius of whose base is 7 m and heights is 24 m?a)120 mb)110 mc)125 md)130 mCorrect answer is option 'B'. Can you explain this answer?
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