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If the radius of the inner circle is one-fifth of the radius of the ou

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If the radius of the inner circle is one-fifth of the radius of the ou  [#permalink]

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New post 22 Aug 2018, 03:48
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If the radius of the inner circle is one-fifth of the radius of the outer circle, what is the ratio of the circumference of the inner circle to that of the outer circle?

A. 1 : 25
B. 1 : 5
C. 2 : 5
D. 5 : 2
E. 5 : 1


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image001.jpg
image001.jpg [ 4.25 KiB | Viewed 763 times ]

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Re: If the radius of the inner circle is one-fifth of the radius of the ou  [#permalink]

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New post 22 Aug 2018, 03:54
Let the radius of the inner circle be r.

Let the radius of the outer circle be R.

Given r = 1/5R. 5r = R

Circumference of smaller circle = 2πr.
Circumference of bigger circle = 2πR.

2πr:2πR.
2πr:2π(5r)
Ratio is 1:5

B is the answer

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If the radius of the inner circle is one-fifth of the radius of the ou  [#permalink]

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New post 22 Aug 2018, 04:05
Bunuel wrote:
Image
Note: Figure not drawn to scale.

If the radius of the inner circle is one-fifth of the radius of the outer circle, what is the ratio of the circumference of the inner circle to that of the outer circle?

A. 1 : 25
B. 1 : 5
C. 2 : 5
D. 5 : 2
E. 5 : 1


Attachment:
image001.jpg


Given, \(r_{i}=\frac{r_{o}}{5}\)
Or, \(\frac{r_{i}}{r_{o}}=\frac{1}{5}\)
ratio of the circumference of the inner circle to that of the outer circle=\(\frac{2\pi*r_{i}}{2\pi*r_{o}}\)=\(\frac{r_{i}}{r_{o}}\)=\(\frac{1}{5}\)

Ans. (B)
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Re: If the radius of the inner circle is one-fifth of the radius of the ou  [#permalink]

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New post 22 Aug 2018, 09:09
Ratio of circumference of inner circle to the outer circle is equal to the ratio of radius of inner circle to the outer circle

r= \(\frac{1}{5}\)R= \(\frac{r}{R}\)= \(\frac{1}{5}\)

Answer: B.
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Re: If the radius of the inner circle is one-fifth of the radius of the ou  [#permalink]

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New post 22 Aug 2018, 10:21
Bunuel wrote:
Image
Note: Figure not drawn to scale.

If the radius of the inner circle is one-fifth of the radius of the outer circle, what is the ratio of the circumference of the inner circle to that of the outer circle?

A. 1 : 25
B. 1 : 5
C. 2 : 5
D. 5 : 2
E. 5 : 1


Attachment:
image001.jpg



given R = 5r

c1 = 2pir
c2 = 2piR
substituting the value
\(\frac{c1}{c2}\) =\(\frac{1}{5}\)
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Re: If the radius of the inner circle is one-fifth of the radius of the ou  [#permalink]

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New post 22 Aug 2018, 10:40
Circumference varies linearly with radius

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Re: If the radius of the inner circle is one-fifth of the radius of the ou  [#permalink]

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New post 26 Aug 2018, 18:26
Bunuel wrote:
Image
Note: Figure not drawn to scale.

If the radius of the inner circle is one-fifth of the radius of the outer circle, what is the ratio of the circumference of the inner circle to that of the outer circle?

A. 1 : 25
B. 1 : 5
C. 2 : 5
D. 5 : 2
E. 5 : 1


Attachment:
image001.jpg


We can let the radius of the inner circle = 1, thus the radius of the outer circle = 5. Furthermore, the circumferences of the inner and outer circles are 2π and 10π, respectively; thus the ratio is

2π/10π = ⅕ , or 1 : 5.

Alternate Solution:

The ratio of the two radii is 1 : 5. Since the circumference of a circle is a linear function of the radius, then the ratio of the circumferences of the two circles remains unchanged from that of the radii, and it is still 1 : 5.

Answer: B
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Re: If the radius of the inner circle is one-fifth of the radius of the ou   [#permalink] 26 Aug 2018, 18:26
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