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# What will be the percentage increase in the area of a circle

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CEO
Joined: 21 Jan 2007
Posts: 2736

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What will be the percentage increase in the area of a circle [#permalink]

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16 Oct 2007, 12:52
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What will be the percentage increase in the area of a circle if the perimeter of the circle grows by 10%?

20%
21%
36%
40%
44%

Kudos [?]: 1023 [0], given: 4

Manager
Joined: 19 Aug 2007
Posts: 168

Kudos [?]: 62 [0], given: 0

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16 Oct 2007, 13:00
assume that the circumference was 10xpi, then it moved up by ten percent to 11 x pi

circumference is 2 pi r so when circumference is 10pi, then r is 5 and when its 11 pi, then r is 5.5.

when r was 5 then the area is 25 x pi, and when r is 5.5 the area is 5.5 * 5.5 = 30.25 x pi.

so 25 to 30.25 is an increase of 21%

B

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CEO
Joined: 21 Jan 2007
Posts: 2736

Kudos [?]: 1023 [0], given: 4

Location: New York City
Re: PS Area - Circumference [#permalink]

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16 Oct 2007, 13:07
bmwhype2 wrote:
What will be the percentage increase in the area of a circle if the perimeter of the circle grows by 10%?

20%
21%
36%
40%
44%

perimeter = circumference = pi*D = 2*pi*R
if the perimeter increases 10% ==> 2*pi*(1.1*R)

the 2 and pi are constants.

area of a circle = pi *Rsquared
= pi * (1.1r)^2
= pi * 1.21 *Rsquared

21 percent increase

Kudos [?]: 1023 [0], given: 4

Intern
Joined: 16 Oct 2007
Posts: 22

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Re: PS Area - Circumference [#permalink]

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16 Oct 2007, 14:18
cir = 2pir
cir incr by 10% ie new cir = 1.1 cir
i.e new r = 1.1 of old rad (remember cir directly prop to radius all other are const)

area = pi r(square)
i.e re rad = sq of old rad i.e. sq(1.1) = 1.21

1.21 is 21 % increase.

bmwhype2 wrote:
What will be the percentage increase in the area of a circle if the perimeter of the circle grows by 10%?

20%
21%
36%
40%
44%

Kudos [?]: [0], given: 0

Re: PS Area - Circumference   [#permalink] 16 Oct 2007, 14:18
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# What will be the percentage increase in the area of a circle

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