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Math Expert V
Joined: 02 Sep 2009
Posts: 58396
What is the area of a circle whose circumference is π?  [#permalink]

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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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Director  G
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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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
Answer A => π/4
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e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3078
Re: What is the area of a circle whose circumference is π?  [#permalink]

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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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Senior Manager  P
Joined: 15 Feb 2018
Posts: 372
What is the area of a circle whose circumference is π?  [#permalink]

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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

$$A=\frac{π^2}{4π}$$
$$A=\frac{π}{4}$$
Board of Directors D
Status: QA & VA Forum Moderator
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Posts: 4777
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GPA: 3.5
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Re: What is the area of a circle whose circumference is π?  [#permalink]

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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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How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only ) Re: What is the area of a circle whose circumference is π?   [#permalink] 20 Jan 2019, 03:02
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What is the area of a circle whose circumference is π?

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