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# The area of a circle is increased by 800%. By what percent

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Joined: 27 Mar 2013
Posts: 36
The area of a circle is increased by 800%. By what percent  [#permalink]

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Updated on: 27 May 2013, 02:28
3
7
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Difficulty:

45% (medium)

Question Stats:

59% (01:04) correct 41% (01:11) wrong based on 202 sessions

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The area of a circle is increased by 800%. By what percent has the diameter of the circle increased?

(A) 100%
(B) 200%
(C) 300%
(D) 600%
(E) 800%

Originally posted by gmatquant25 on 27 May 2013, 02:11.
Last edited by gmatquant25 on 27 May 2013, 02:28, edited 2 times in total.
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Posts: 51233
Re: The area of a circle is increased by 800%. By what percent  [#permalink]

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27 May 2013, 02:21
2
gmatquant25 wrote:
The area of a circle is increased by 800%. By what percent has the diameter of the circle increased?

(A) 100%
(B) 200%
(C) 300%
(D) 600%

The area of the circle is increased by 800%, thus the area is increased 9 times.

The area of a circle it proportional to the square of the diameter ($$area=\pi{\frac{d^2}{4}}$$), therefore the diameter must increase 3 times (diameter increase 3 times = area increase 9 times), which is increase by 200%.

Similar questions to practice:
at-a-certain-pizza-parlor-the-diameter-140460.html
the-weight-of-a-hollow-sphere-is-directly-dependent-on-its-142327.html

Hope it helps.
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Re: The area of a circle is increased by 800%. By what percent  [#permalink]

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21 Nov 2013, 15:07
Another approach. Firstly, given that area increased by 800%. It means that if we take initial area as 100% then final area is (100%+800%=)900%. Now, make two equations:$$pi(R^2)=100$$-----> R=10/$$\sqrt{pi}$$. Likewise, $$pi(r^2)=900$$---->r=30/$$\sqrt{pi}$$. Answer is $$\frac{(r-R}{R)}$$*100=200%.
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Re: The area of a circle is increased by 800%. By what percent  [#permalink]

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21 Nov 2013, 16:40
How did you figure "The area of the circle is increased by 800%, thus the area is increased 9 times" ?
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Posts: 51233
Re: The area of a circle is increased by 800%. By what percent  [#permalink]

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22 Nov 2013, 00:24
gmat978 wrote:
How did you figure "The area of the circle is increased by 800%, thus the area is increased 9 times" ?

(area)*(1+800/100) = (area)*9.

Hope it's clear.
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Re: The area of a circle is increased by 800%. By what percent  [#permalink]

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22 Feb 2015, 14:07
1
Hi All,

There's a practical way to prove the correct answer. We can TEST VALUES, using the answer choices to limit our TESTs:

If we have a circle with....
A diameter of 2
it's radius = 1
it's area = (1^2)pi = 1pi

If we increase that diameter 100%, we have....
A diameter of 4
it's radius = 2
it's area = (2^2)pi = 4pi
This area has increased (4pi - 1pi)/1pi = 3pi/1pi = 3 = 300%

If we increase the diameter 200%, we have...
A diameter of 6
it's area = 3
it's area = (3^2)pi = 9pi
This area has increased (9pi - 1pi)/1pi = 8pi/1pi = 8 = 800%

This is a MATCH for what we're looking for!

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Re: The area of a circle is increased by 800%. By what percent  [#permalink]

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25 Jan 2016, 18:53
i plugged in numbers...
r=1, diameter is 2.

area is pi. thus, new area would be 9pi.
9pi -> r=3, and diameter is 6.

to find the percent increase:
(6-2)/2 *100% = 4/2 *100% = 200%
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Re: The area of a circle is increased by 800%. By what percent  [#permalink]

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05 Dec 2018, 10:42
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Re: The area of a circle is increased by 800%. By what percent &nbs [#permalink] 05 Dec 2018, 10:42
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# The area of a circle is increased by 800%. By what percent

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