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# If the radius of a circle is decreased by 30 percent, by what percent

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Math Expert
Joined: 02 Sep 2009
Posts: 50002
If the radius of a circle is decreased by 30 percent, by what percent  [#permalink]

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14 Nov 2017, 23:38
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25% (medium)

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82% (00:58) correct 18% (01:16) wrong based on 62 sessions

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If the radius of a circle is decreased by 30 percent, by what percent will the area of the circular region be decreased?

(A) 15%
(B) 49%
(C) 51%
(D) 60%
(E) 90%

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Joined: 12 Feb 2017
Posts: 70
Re: If the radius of a circle is decreased by 30 percent, by what percent  [#permalink]

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14 Nov 2017, 23:45
let the radius of circle be R
Area of the circle= 3.14 * R^2
Now, radius is decreased by 30%
New radius of circle would be 0.7R
Hence,
New Area= 3.14*(0.7R)^2
New Area= 0.49 * 3.14*R^2

Therefore, New area of the circle would be 51% less than that of original one.

Kudos if it helps.
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Joined: 22 May 2016
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If the radius of a circle is decreased by 30 percent, by what percent  [#permalink]

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15 Nov 2017, 04:18
Bunuel wrote:
If the radius of a circle is decreased by 30 percent, by what percent will the area of the circular region be decreased?

(A) 15%
(B) 49%
(C) 51%
(D) 60%
(E) 90%

Choose values

Let the original radius = 10
Original area is $$\pi*r^2=100\pi$$

The radius is decreased by 30 percent:
.70(10) = 7
New area is $$\pi*r^2=49\pi$$

Percent decrease:
$$\frac{New-Old}{Old} * 100$$

$$\frac{100-49}{100}=\frac{51}{100} * 100 = 51$$ percent

Scale Factor
Length * Length = Area
Scale factor = (1 - .30) = .70

When area (length * length) is decreased by a scale factor, the scale factor, squared (because it is used for both lengths)*, can be used to calculate the percent change.

$$(.7)^2 = .49$$
Original = $$1$$
Percent decrease:
$$(1 - .49) = .51 * 100 = 51$$ percent

That is:
Length * length = area = (scale factor)$$^2$$ for change
$$\pi$$ is constant
Radius is the length affected twice by scale factor.
Original, $$r^2=(r)(r)$$ to new, $$(.7r)^2=(.7r)(.7r)$$

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Re: If the radius of a circle is decreased by 30 percent, by what percent  [#permalink]

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15 Nov 2017, 08:38
Bunuel wrote:
If the radius of a circle is decreased by 30 percent, by what percent will the area of the circular region be decreased?

(A) 15%
(B) 49%
(C) 51%
(D) 60%
(E) 90%

$$-30 - 30 + \frac{(-30*-30)}{100} = 51$$%

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Thanks and Regards

Abhishek....

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Re: If the radius of a circle is decreased by 30 percent, by what percent &nbs [#permalink] 15 Nov 2017, 08:38
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