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By what percentage does the curved surface area of a cone increase if its radius and the height increase proportionately to 4 times the original sizes?
- a)1500%
- b)1300%
- c)1600%
- d)1400%
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
By what percentage does the curved surface area of a cone increase if ...
Initial curved surface area of the cone = -πr1/1 where r^ is the initial radius and A| is the initial slant height. New curved surface area =πr2l2
It is given that, r2 = 4r<| and h2 = 4
Slant height l12 = r12 + h12 l22 = r22 + h22 = (4r1)2 + (4h1)2 =
16(r12+ h12)
= 16/12
Thus, I2 = 4l1
New curved surface area = πr2l2
Hence, option 1.
Most Upvoted Answer
By what percentage does the curved surface area of a cone increase if ...
Explanation:
Given:
Radius and height increase proportionately to 4 times the original sizes.
Formula for Curved Surface Area of a Cone:
Curved Surface Area = πrℓ
Initial Curved Surface Area:
Let the initial radius be 'r' and height be 'h'.
Initial CSA = πr√(r^2 + h^2)
Final Curved Surface Area:
After the increase, the new radius = 4r and new height = 4h.
Final CSA = π(4r)√((4r)^2 + (4h)^2)
= π(4r)(4√(r^2 + h^2))
= 16πr√(r^2 + h^2)
Percentage Increase:
Percentage Increase = ((Final CSA - Initial CSA) / Initial CSA) * 100
= ((16πr√(r^2 + h^2) - πr√(r^2 + h^2)) / πr√(r^2 + h^2)) * 100
= (15πr√(r^2 + h^2) / πr√(r^2 + h^2)) * 100
= 15 * 100
= 1500%
Therefore, the curved surface area of the cone increases by 1500% when the radius and height increase proportionately to 4 times the original sizes. Hence, option 'A' is the correct answer.
Given:
Radius and height increase proportionately to 4 times the original sizes.
Formula for Curved Surface Area of a Cone:
Curved Surface Area = πrℓ
Initial Curved Surface Area:
Let the initial radius be 'r' and height be 'h'.
Initial CSA = πr√(r^2 + h^2)
Final Curved Surface Area:
After the increase, the new radius = 4r and new height = 4h.
Final CSA = π(4r)√((4r)^2 + (4h)^2)
= π(4r)(4√(r^2 + h^2))
= 16πr√(r^2 + h^2)
Percentage Increase:
Percentage Increase = ((Final CSA - Initial CSA) / Initial CSA) * 100
= ((16πr√(r^2 + h^2) - πr√(r^2 + h^2)) / πr√(r^2 + h^2)) * 100
= (15πr√(r^2 + h^2) / πr√(r^2 + h^2)) * 100
= 15 * 100
= 1500%
Therefore, the curved surface area of the cone increases by 1500% when the radius and height increase proportionately to 4 times the original sizes. Hence, option 'A' is the correct answer.
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By what percentage does the curved surface area of a cone increase if its radius and the height increase proportionately to 4 times the original sizes?a)1500%b)1300%c)1600%d)1400%Correct answer is option 'A'. Can you explain this answer?
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