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

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Joined: 02 Sep 2009
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The relationship between the area A of a circle and its circumference  [#permalink]

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16 Jul 2018, 20:09
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Difficulty:

25% (medium)

Question Stats:

81% (00:52) correct 19% (01:41) wrong based on 74 sessions

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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. $$4\pi^2$$

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Re: The relationship between the area A of a circle and its circumference  [#permalink]

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16 Jul 2018, 21:19
Bunuel wrote:
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. $$4\pi^2$$

Given, $$k=\frac{A}{C^2}$$=$$\frac{πr^2}{(2πr)^2}$$=$$\frac{1}{4\pi}$$

Ans. (A)
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Re: The relationship between the area A of a circle and its circumference  [#permalink]

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16 Jul 2018, 22:58
Bunuel wrote:
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 = kC^2
k = A / C^2 ; where, Area (A) = πR^2 and Circumferance (C) = 2πR

Therefore,
k = πR^2 / (2πR)^2
k = 1 / 4π

Hence, A.
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Re: The relationship between the area A of a circle and its circumference  [#permalink]

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17 Jul 2018, 06:14
Bunuel wrote:
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. $$4\pi^2$$

$$A = πr^2$$

$$C = 2πr$$

Since, $$A=kC^2$$

We have $$πr^2 = k(2πr)^2$$

Or, $$πr^2 = 4kπr^2$$

Or, $$1 = 4k$$

So, $$k = \frac{1}{4}$$ , Answer must be (C)
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The relationship between the area A of a circle and its circumference  [#permalink]

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17 Jul 2018, 12:17
Abhishek009 wrote:
Bunuel wrote:
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. $$4\pi^2$$

$$A = πr^2$$

$$C = 2πr$$

Since, $$A=kC^2$$

We have $$πr^2 = k(2πr)^2$$

Or, $$πr^2 = 4kπr^2$$

Or, $$1 = 4k$$

So, $$k = \frac{1}{4}$$ , Answer must be (C)

When you open the brackets you have $$π^2$$, not $$π$$
The relationship between the area A of a circle and its circumference &nbs [#permalink] 17 Jul 2018, 12:17
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