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# If the radius of a circle is increased by 6%, then the area of the cir

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If the radius of a circle is increased by 6%, then the area of the cir [#permalink]

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29 Oct 2017, 00:17
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25% (medium)

Question Stats:

80% (00:52) correct 20% (00:57) wrong based on 50 sessions

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If the radius of a circle is increased by 6%, then the area of the circle is increased by

(A) .36%
(B) 3.6%
(C) 6%
(D) 12.36%
(E) 36%
[Reveal] Spoiler: OA

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Re: If the radius of a circle is increased by 6%, then the area of the cir [#permalink]

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29 Oct 2017, 07:44
Bunuel wrote:
If the radius of a circle is increased by 6%, then the area of the circle is increased by

(A) .36%
(B) 3.6%
(C) 6%
(D) 12.36%
(E) 36%

Area of the Circle = $$πr^2$$

So, Percentage change in area of the Circle is 6 + 6 +6*6/100 = 12.36%

Thus, correct answer will be (D) 12.36%
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If the radius of a circle is increased by 6%, then the area of the cir [#permalink]

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29 Oct 2017, 20:11
Bunuel wrote:
If the radius of a circle is increased by 6%, then the area of the circle is increased by

(A) .36%
(B) 3.6%
(C) 6%
(D) 12.36%
(E) 36%

Increase in area =
((scale factor)$$^2$$ - 1) * 100

6 percent increase = 1.06 scale factor

(1.06)$$^2$$ = 1.1236
(1.1236 - 1) * 100 =
(.1236 * 100) = 12.36 percent

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Re: If the radius of a circle is increased by 6%, then the area of the cir [#permalink]

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29 Oct 2017, 21:24
area of the circle is pi*r^2
so percentage increase equal to (1.06)^2 = 12.36 %
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Re: If the radius of a circle is increased by 6%, then the area of the cir [#permalink]

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31 Oct 2017, 15:15
Bunuel wrote:
If the radius of a circle is increased by 6%, then the area of the circle is increased by

(A) .36%
(B) 3.6%
(C) 6%
(D) 12.36%
(E) 36%

We can let the original area = πr^2; thus, the new area is π(1.06r)^2 = π(1.1236)r^2.

We use the percent increase formula: (New - Old)/Old x 100. Thus, the area is increased by:

[π(1.1236)r^2 - πr^2]/πr^2 x 100

[0.01236πr^2/]/πr^2 x 100 = 12.36%

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Re: If the radius of a circle is increased by 6%, then the area of the cir   [#permalink] 31 Oct 2017, 15:15
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