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# If the diameter of a circle increases by 50 percent, by what percent

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Joined: 02 Sep 2009
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If the diameter of a circle increases by 50 percent, by what percent  [#permalink]

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10 Jan 2019, 02:27
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If the diameter of a circle increases by 50 percent, by what percent will the area of the circle increase?

A. 25%
B. 50%
C. 100%
D. 125%
E. 225%

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Re: If the diameter of a circle increases by 50 percent, by what percent  [#permalink]

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10 Jan 2019, 02:57
If the diameter increases 50%, the radius also increases 50%.
The area would remain Pi(r^2)
Say for example Radius increases from 10 to 15
the area would increase from 100pi to 225pi.
therefore 125% increase.
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Re: If the diameter of a circle increases by 50 percent, by what percent  [#permalink]

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10 Jan 2019, 05:06
Bunuel wrote:
If the diameter of a circle increases by 50 percent, by what percent will the area of the circle increase?

A. 25%
B. 50%
C. 100%
D. 125%
E. 225%

area = 4pi
50% increase in dia = 4*1.5 = 6
area = 9pi
% change in area = 9pi-4Pi/ 4 pi = 125 % IMO D
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If the diameter of a circle increases by 50 percent, by what percent  [#permalink]

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10 Jan 2019, 06:32

Solution

Given:
• The diameter of a circle increases by 50%

To find:
• The percentage increase in area of the circle

Approach and Working:
Let ‘d‘ be the initial diameter
• Area = $$ᴨ\frac{d^2}{4}$$ = A

New diameter = $$d + \frac{d}{2} = \frac{3d}{2}$$
• Area = $$ᴨ(\frac{3d}{2})^2/4 = 9ᴨ\frac{d^2}{16} = \frac{9A}{4}$$

Percentage increase in area = $$[(\frac{9A}{4} – A)/A] *100 = 125$$%

Hence, the correct answer is Option D

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Re: If the diameter of a circle increases by 50 percent, by what percent  [#permalink]

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20 Jun 2020, 14:30
Bunuel wrote:
If the diameter of a circle increases by 50 percent, by what percent will the area of the circle increase?

A. 25%
B. 50%
C. 100%
D. 125%
E. 225%

Solution:

If the diameter of a circle increases by 50 percent, the radius also increases by 50 percent. If we let the original radius = 10, the new radius = 15. Thus, we have:

Area of the original circle = 10^2 x π = 100π

Area of the new circle = 15^2 x π = 225π

We use the percent change formula: (New - Old) / Old x 100. Therefore, the area of the circle increases by

(225π - 100π)/(100π) x 100 = 125π/π = 125 percent

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Re: If the diameter of a circle increases by 50 percent, by what percent   [#permalink] 20 Jun 2020, 14:30