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# The area of circle W is 16π and the area of circle Z is 4π. What is th

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Joined: 02 Sep 2009
Posts: 50619
The area of circle W is 16π and the area of circle Z is 4π. What is th  [#permalink]

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15 Jul 2018, 07:40
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Difficulty:

5% (low)

Question Stats:

94% (00:37) correct 6% (00:23) wrong based on 33 sessions

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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

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Re: The area of circle W is 16π and the area of circle Z is 4π. What is th  [#permalink]

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15 Jul 2018, 08:02
+1 for A.

Area W = 16π = πR^2 ---> Solving R = 4
Area Z = 4π = πr^2 ---> Solving r = 2

Circumference of W / Circumference of Z = (2*π*R) / (2*π*r) = (2*π*4) / (2*π*2) = 2/1

Hence, A.
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Re: The area of circle W is 16π and the area of circle Z is 4π. What is th  [#permalink]

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15 Jul 2018, 10:50
Bunuel 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

Area of circle w = 16π

So, π r^2 = 16 π

r = 4.

Area of circle z = 4π

So, πr^2 = 4π

r = 2.

Ratio of the circumference = circumference of w / circumference of z

= 2πr / 2πr

= 4 / 2

= 2 : 1

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The area of circle W is 16π and the area of circle Z is 4π. What is th  [#permalink]

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16 Jul 2018, 08:04
Bunuel 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

$$W = 16π$$ ; So $$R = 4$$

$$Z = 4π$$ ; So $$r = 2$$

We know Ratio of Circumferences is The ratio of the Radii ( As , $$2πR: 2πr = R:r)$$

Thus, the ratio of the circumference of W to the circumference of Z is $$4 : 2 = 2:1$$ , Answer must be (A)
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Re: The area of circle W is 16π and the area of circle Z is 4π. What is th  [#permalink]

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19 Jul 2018, 11:37
Bunuel 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: The area of circle W is 16π and the area of circle Z is 4π. What is th &nbs [#permalink] 19 Jul 2018, 11:37
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