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# What is the ratio of the inner circle's circumference to the outer cir

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Math Expert
Joined: 02 Sep 2009
Posts: 50572
What is the ratio of the inner circle's circumference to the outer cir  [#permalink]

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14 Sep 2018, 00:23
00:00

Difficulty:

45% (medium)

Question Stats:

75% (01:05) correct 25% (01:37) wrong based on 24 sessions

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What is the ratio of the inner circle's circumference to the outer circle's circumference, if the inner circle's area is 80% of the outer circle's area?

A. 4 : 5

B. $$2 : \sqrt{5}$$

C. $$\sqrt{5}: 2$$

D. $$4 \pi: \sqrt{5}$$

E. It cannot be determined from the information given.

Attachment:

image018.jpg [ 3.86 KiB | Viewed 376 times ]

_________________
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Joined: 02 Sep 2015
Posts: 42
What is the ratio of the inner circle's circumference to the outer cir  [#permalink]

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Updated on: 14 Sep 2018, 09:46
Area Of Inner circle with radius "r" = 80/100 * Area of outer circle with radius "R"
$$\pi * r^2 = \frac{80}{100} * \pi * R^2$$
cancel pi and take square root on both sides
$$r = \sqrt\frac{8}{10} * R$$
$$\frac{r}{R} = \frac{2}{\sqrt5}$$
Multiply $$2*\pi$$ in numerator and denominator of LHS to get the circumference
$$\frac{2*\pi*r}{2*\pi*R} = \frac{2}{\sqrt5}$$

Originally posted by magbot on 14 Sep 2018, 09:10.
Last edited by magbot on 14 Sep 2018, 09:46, edited 1 time in total.
Intern
Joined: 28 Jun 2018
Posts: 46
Re: What is the ratio of the inner circle's circumference to the outer cir  [#permalink]

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14 Sep 2018, 09:30
I don't get r=810−−√∗Rr=810∗R
rR=25√

How did we get that value? magbot
Intern
Joined: 02 Sep 2015
Posts: 42
Re: What is the ratio of the inner circle's circumference to the outer cir  [#permalink]

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14 Sep 2018, 09:47
Director
Joined: 04 Sep 2015
Posts: 510
Location: India
WE: Information Technology (Computer Software)
Re: What is the ratio of the inner circle's circumference to the outer cir  [#permalink]

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14 Sep 2018, 10:39
given, the area of C1 is 80% of C2

lets put it this way,

C1/C2=80/100

thus, pi*R1*R1/pi*R2*R2= 80/100

R1square/R2square=4/5

R1/R2=2/root5

for crcmfrnc

2piR1/2piR2=2/root5

or 2/root5
Re: What is the ratio of the inner circle's circumference to the outer cir &nbs [#permalink] 14 Sep 2018, 10:39
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