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# What is the circumference of a circle whose area is 49π?

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Math Expert
Joined: 02 Sep 2009
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What is the circumference of a circle whose area is 49π?  [#permalink]

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17 Jan 2019, 04:48
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Difficulty:

5% (low)

Question Stats:

95% (00:33) correct 5% (00:20) wrong based on 28 sessions

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What is the circumference of a circle whose area is 49π?

A 7π
B 14π
C 24.5π
D 35π
E 49π

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Joined: 09 Mar 2018
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Location: India
Re: What is the circumference of a circle whose area is 49π?  [#permalink]

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17 Jan 2019, 05:07
Bunuel wrote:
What is the circumference of a circle whose area is 49π?

A 7π
B 14π
C 24.5π
D 35π
E 49π

Area = 49 π
π r^2 = 49 π
r = 7

C = 2π7
C =14 π

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Re: What is the circumference of a circle whose area is 49π?  [#permalink]

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17 Jan 2019, 06:35

Solution

Given:
• Area of the circle = 49ᴨ

To find:
• The circumference of the circle

Approach and Working:
Area = $$ᴨr^2 = 49ᴨ$$
• Implies, $$r^2 = 49$$
• Thus, r = 7

Circumference = 2ᴨr = 2ᴨ * 7 = 14ᴨ

Hence, the correct answer is Option B

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Re: What is the circumference of a circle whose area is 49π?  [#permalink]

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19 Jan 2019, 19:23
Finding area from circumference seems to be asked frequently, so it can't hurt to learn the formula

$$Area = \frac{C^2}{(4π)}$$

We are given that A=49π

$$49π = \frac{C^2}{(4π)}$$
$$49π·4π = C^2$$
$$7^2·2^2·π^2=C^2$$
$$7·2·π=C=14π$$
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Re: What is the circumference of a circle whose area is 49π?  [#permalink]

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20 Jan 2019, 02:54
Bunuel wrote:
What is the circumference of a circle whose area is 49π?

A 7π
B 14π
C 24.5π
D 35π
E 49π

$$πr^2 = 49π$$

So, $$r = 7$$

Thus, the circumference will be $$2*π*7 = 14π$$ , Answer must be (B) 14π
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Re: What is the circumference of a circle whose area is 49π?   [#permalink] 20 Jan 2019, 02:54
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