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

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QOTD #8 The area of circle W is 16π and the area of circle Z [#permalink] New post 14 Aug 2016, 06:59
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86% (00:33) correct 13% (00:31) wrong based on 37 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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Re: QOTD #8 The area of circle W is 16π and the area of circle Z [#permalink] New post 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

Answer: A
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Re: QOTD #8 The area of circle W is 16π and the area of circle Z [#permalink] New post 12 Jun 2019, 09:08
Expert's post
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

Practice Questions
Question: 10
Page: 151


Area of circle = πr²

Area of circle W is 16π
We can write: 16π = πr²
Divide both sides by π to get: 16 = r²
Solve: r = 4 or r = -4
Since the radius can't be negative, we know that the radius of circle W is 4

Area of circle Z is 4π
We can write: = πr²
Divide both sides by π to get: 4 = r²
Solve: r = 2 or r = -2
Since the radius can't be negative, we know that the radius of circle Z is 2


What is the ratio of the circumference of W to the circumference of Z ?
Circumference of circle = 2πr

So, the circumference of circle W = (2)(π)(4) =
The circumference of circle Z = (2)(π)(2) =

Ratio = / = 2/1 = 2 to 1

Answer: A

Cheers,
Brent
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Re: QOTD #8 The area of circle W is 16π and the area of circle Z   [#permalink] 12 Jun 2019, 09:08
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QOTD #8 The area of circle W is 16π and the area of circle Z

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