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# The relationship between the area A of a circle and its circ

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Retired Moderator
Joined: 07 Jun 2014
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GRE 1: Q167 V156
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The relationship between the area A of a circle and its circ [#permalink]  27 Dec 2015, 20:03
Expert's post
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Question Stats:

77% (00:58) correct 22% (01:38) wrong based on 83 sessions
The relationship between the area A of a circle and its circumference C is given by the formula $$A=kC^2$$, where k is a constant. What is the value of k ?

A. $$\frac{1}{4\pi}$$

B. $$\frac{1}{2\pi}$$

C. $$\frac{1}{4}$$

D. $$2\pi$$

E. $$4\pi^2$$

Here $$\pi =3.14$$

Practice Questions
Question: 11
Page: 158
Difficulty: hard
[Reveal] Spoiler: OA

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Sandy
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Retired Moderator
Joined: 07 Jun 2014
Posts: 4804
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 163

Kudos [?]: 2770 [1] , given: 394

Re: relationship between the area A of a circle [#permalink]  27 Dec 2015, 20:25
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Expert's post
Let r be the radius of the circle.

Now by definition $$C= 2*pi*r$$ and $$C^2= 4* pi^2 * r^2$$.

Also $$A = pi * r^2$$.

Now $$\frac{A}{C^2}= \frac{pi}{4*pi^2}$$
or $$\frac{A}{C^2}= \frac{1}{4*pi}$$

Now k=$$\frac{1}{4*pi}$$.
_________________

Sandy
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Re: relationship between the area A of a circle   [#permalink] 27 Dec 2015, 20:25
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