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# If the radius of a circle is decreased by 10%, by what percent is its

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Math Expert
Joined: 02 Sep 2009
Posts: 44298
If the radius of a circle is decreased by 10%, by what percent is its [#permalink]

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08 Mar 2018, 02:18
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If the radius of a circle is decreased by 10%, by what percent is its area decreased?

(A) 10

(B) 19

(C) 21

(D) 79

(E) 81
[Reveal] Spoiler: OA

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Math Expert
Joined: 02 Sep 2009
Posts: 44298
Re: If the radius of a circle is decreased by 10%, by what percent is its [#permalink]

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08 Mar 2018, 02:18
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Bunuel wrote:
If the radius of a circle is decreased by 10%, by what percent is its area decreased?

(A) 10

(B) 19

(C) 21

(D) 79

(E) 81

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Re: If the radius of a circle is decreased by 10%, by what percent is its [#permalink]

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08 Mar 2018, 02:25
Bunuel wrote:
If the radius of a circle is decreased by 10%, by what percent is its area decreased?

(A) 10

(B) 19

(C) 21

(D) 79

(E) 81

We'll pick an easy number which can help us make the calculation.
This is an Alternative approach.

Say the original radius was 10. Then the original area is pi*10^2 = 100pi
If the radius decreases by 10% it is now 9. Then the new area is pi*9^2 =81pi
This is a decrease of 100pi - 81pi = 19pi.
Since 19pi 19% of 100pi, our answer is 19%.

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Joined: 22 May 2016
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If the radius of a circle is decreased by 10%, by what percent is its [#permalink]

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08 Mar 2018, 10:58
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Bunuel wrote:
If the radius of a circle is decreased by 10%, by what percent is its area decreased?

(A) 10

(B) 19

(C) 21

(D) 79

(E) 81

Scale factor:
All changes in dimension of a figure have to do with length. Length is increased or decreased by a scale factor, $$k$$

Decrease in one length only (one dimension) = multiply by $$k$$

Decrease in area?
Area = length*length (two dimensions)
Multiply by $$(k*k)= k^2$$

Original area = A
New area = (original area)*($$k^2$$)
(.9)*(.9)*(A) = .81A

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

$$(\frac{-.81A-A}{A}*100) =\frac{|-.19|}{1}*100= 19$$
% decrease

* Decrease in volume, e.g. cube, if change is uniform = (length * length * length) = multiply by $$(k*k*k) = k^3$$
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If the radius of a circle is decreased by 10%, by what percent is its   [#permalink] 08 Mar 2018, 10:58
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