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

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

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17 Jan 2019, 04:47
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Difficulty:

25% (medium)

Question Stats:

76% (00:44) correct 24% (00:43) wrong based on 28 sessions

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

A π/4
B π/2
C π
D 2π
E 4π

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Joined: 09 Mar 2018
Posts: 994
Location: India
Re: What is the area of a circle whose circumference is π?  [#permalink]

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

A π/4
B π/2
C π
D 2π
E 4π

C = 2 πr
r = 1/2

Area = π r^2
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Re: What is the area of a circle whose circumference is π?  [#permalink]

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17 Jan 2019, 06:39

Solution

Given:
• Circumference of a circle = ᴨ

To find:
• Area of the circle

Approach and Working:
Circumference = 2ᴨr = ᴨ
• Implies, $$r = \frac{1}{2}$$

Therefore, area = $$ᴨr^2 = ᴨ * (\frac{1}{2})^2 = \frac{ᴨ}{4}$$

Hence, the correct answer is Option A

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

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19 Jan 2019, 19:13
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 C=π

$$A=\frac{π^2}{4π}$$
$$A=\frac{π}{4}$$
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Re: What is the area of a circle whose circumference is π?  [#permalink]

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20 Jan 2019, 03:02
Bunuel wrote:
What is the area of a circle whose circumference is π?

A π/4
B π/2
C π
D 2π
E 4π

$$2πr = π$$

Thus, $$r = \frac{1}{2}$$

So, Area of the Circle is $$\frac{π}{4}$$, Answer must be (A)
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Re: What is the area of a circle whose circumference is π?   [#permalink] 20 Jan 2019, 03:02
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