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If the circumference of circle O is 5 times the circum

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If the circumference of circle O is 5 times the circum [#permalink] New post   07 Sep 2020, 04:55
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If the circumference of circle O is 5 times the circumference of circle O′, then the area of circle O is how many times the area of circle O′?


Show: :: OA
25 times
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Re: If the circumference of circle O is 5 times the circum [#permalink] New post   07 Sep 2020, 04:55
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Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
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Re: If the circumference of circle O is 5 times the circum [#permalink] New post   08 Sep 2020, 05:29
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Is this the correct picture? Because I can't see O and O' in it... Thanks!
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Re: If the circumference of circle O is 5 times the circum [#permalink] New post   08 Sep 2020, 05:37
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Sorry I have uploaded the wrong figure related to another question.

Thank you. Fixed
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Re: If the circumference of circle O is 5 times the circum [#permalink] New post   11 Sep 2020, 01:52
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If the circumference of circle O is 5 times the circumference of circle O′, then the area of circle O is how many times the area of circle O′?


Show: :: OA
25 times



Circumference= 2*pi*r

let the radius of o' be 1, so circumference is 2*pi*1=2Pi
so the circumference of circle O is 5 times 2pi=10*pi

radius of circle O= sq rt (5)

(Area of O)/(area of O')= ((sq rt (5))^2)/1 = 25
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Re: If the circumference of circle O is 5 times the circum [#permalink] New post   13 Sep 2020, 00:48
C1:C2 =5:1
this means
r1:r2 =5:1 (C=2π*r)
as A = πr²
A1:A2 = (5*5)/(1*1) = 25
so area of cirlce O is 25 times area of O'
(here suffix 1 is related to circle O and suffix 2 related to circle O')
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