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The ratio of the area of circle \(A\) to the area of circle \(B\) is 4:1. What is the ratio of the circumference of

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by VJesus12 » Mon May 11, 2020 6:32 am
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The ratio of the area of circle \(A\) to the area of circle \(B\) is 4:1. What is the ratio of the circumference of circle \(A\) to the circumference of circle \(B?\)

A. 1:3

B. 1:1

C. 2:1

D. 4:1

E. 8:1

[spoiler]OA=C[/spoiler]

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Re: The ratio of the area of circle \(A\) to the area of circle \(B\) is 4:1. What is the ratio of the circumference of

by Scott@TargetTestPrep » Wed May 13, 2020 8:18 am
VJesus12 wrote: ↑
Mon May 11, 2020 6:32 am
 The ratio of the area of circle \(A\) to the area of circle \(B\) is 4:1. What is the ratio of the circumference of circle \(A\) to the circumference of circle \(B?\)

A. 1:3

B. 1:1

C. 2:1

D. 4:1

E. 8:1

[spoiler]OA=C[/spoiler]

Let the radius of circle A be R and the radius of circle B be r. We can create the equation:

(πR^2) / (πr^2) = 4/1

R^2 / r^2 = 4

R^2 = 4r^2

√(R^2) =√(4r^2)

R = 2r

Now let’s compare the circumferences of the two circles by substituting 2r for R:

(2πR) / (2πr) = R/r = 2r/r = 2/1

Answer: C

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