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# QOTD #8 The area of circle W is 16π and the area of circle Z

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Joined: 07 Jun 2014
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QOTD #8 The area of circle W is 16π and the area of circle Z [#permalink]  14 Aug 2016, 06:59
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76% (00:30) correct 23% (00:31) wrong based on 21 sessions
The area of circle W is 16π and the area of circle Z is 4π. What is the ratio of the circumference of W to the circumference of Z ?

A. 2 to 1
B. 4 to 1
C. 8 to 1
D. 16 to 1
E. 32 to 1

Practice Questions
Question: 10
Page: 151
[Reveal] Spoiler: OA

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Sandy
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GMAT Club Legend
Joined: 07 Jun 2014
Posts: 4749
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 93

Kudos [?]: 1659 [0], given: 396

Re: QOTD #8 The area of circle W is 16π and the area of circle Z [#permalink]  14 Aug 2016, 07:01
Expert's post
Explanation

Recall that if a circle has radius r, then the area of the circle is π$$r^2$$ and the circumference is 2πr. Since the area of circle W is 16π, it follows that π $$r^2$$ = 16π, so $$r^2$$ = 16 and r = 4. Therefore the circumference of circle W is 2π(4), or 8π. Similarly, since the area of circle Z is 4π, it follows that π$$r^2$$ = 4π, so $$r^2$$ = 4 and r = 2. Therefore the circumference of circle Z is 2π(2), or 4π. Thus the ratio of the circumference of W to the circumference of Z is 8π to 4π, or 2 to 1. The correct answer is Choice A.
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Sandy
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Re: QOTD #8 The area of circle W is 16π and the area of circle Z [#permalink]  19 Jul 2018, 11:38
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sandy wrote:
The area of circle W is 16π and the area of circle Z is 4π. What is the ratio of the circumference of W to the circumference of Z ?

A. 2 to 1
B. 4 to 1
C. 8 to 1
D. 16 to 1
E. 32 to 1

We must first determine the radius of each circle. Letting R = the radius of circle W and r = the radius of circle Z, we have:

πR^2 = 16π

R^2 = 16

R = 4

and

πr^2 = 4π

r^2 = 4

r = 2

Using the circle circumference formula C = 2πr, we see that the circumference of circleW is 2πR = 2π(4) = 8π, and the circumference of circle Z is 2πr = 2π(2) = 4π. Thus, the ratio of the circumference of W to the circumference of Z is

8π/4π = 2/1

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Re: QOTD #8 The area of circle W is 16π and the area of circle Z   [#permalink] 19 Jul 2018, 11:38
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