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If the ratio of the circumference of a circle to the area of the same

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If the ratio of the circumference of a circle to the area of the same [#permalink]

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New post 27 Apr 2017, 01:42
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If the ratio of the circumference of a circle to the area of the same circle is 1 to 3, what is the diameter of the circle?

A. 2
B 3
C. 6
D. 12
E. 18
[Reveal] Spoiler: OA

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Re: If the ratio of the circumference of a circle to the area of the same [#permalink]

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New post 27 Apr 2017, 01:45
Let the radius of the cicle be R
2*pi*R / pi*R*R = 1/3
2/R = 1/3
R = 6
Diameter = 2R = 12(Option D)
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Re: If the ratio of the circumference of a circle to the area of the same [#permalink]

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New post 30 Apr 2017, 07:53
I worked backwards by using the answer choices. If we plug in answer choice D:

d=12, then radius = 6 and circumference = 12pi.

now, we can find the area.

A= piR^2 = pi6^2 = 36pi.

circumference: area = 12pi: 36pi reduce this and we get the stated ratio of 1:3
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Re: If the ratio of the circumference of a circle to the area of the same [#permalink]

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Bunuel wrote:
If the ratio of the circumference of a circle to the area of the same circle is 1 to 3, what is the diameter of the circle?

A. 2
B 3
C. 6
D. 12
E. 18


Solution



    • We need to find the Diameter of the circle \(= D\) (assumed)

      o The circumference of the circle is given by \(= 2π*(\frac{D}{2}) = πD\)

      o Area of the circle \(= π*\frac{D^2}{4}\)

    • We are given

      o \(\frac{Area}{Circumference}= \frac{3}{1}\)

      o \(\frac{(πD^2)}{(4πD)} = \frac{3}{1}\)

      o D = 12

    • Hence the correct answer is Option D


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Re: If the ratio of the circumference of a circle to the area of the same [#permalink]

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New post 06 May 2017, 16:29
Bunuel wrote:
If the ratio of the circumference of a circle to the area of the same circle is 1 to 3, what is the diameter of the circle?

A. 2
B 3
C. 6
D. 12
E. 18


We can let r = the radius of the circle and create the following equation:

2πr/πr^2 = 1/3

6πr = πr^2

6r = r^2

6 = r

Thus, the diameter is 2 x 6 = 12.

Answer: D
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Re: If the ratio of the circumference of a circle to the area of the same [#permalink]

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New post 18 May 2017, 03:09
given = 2(pi)r / (pi) r^2 = 1/3 solving for r => r = 6 hence diameter is 2r = 12

Option D is correct
Re: If the ratio of the circumference of a circle to the area of the same   [#permalink] 18 May 2017, 03:09
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