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# If the circumference of a circle is 2x, what is the area of the circle

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Math Expert
Joined: 02 Sep 2009
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If the circumference of a circle is 2x, what is the area of the circle  [#permalink]

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05 Sep 2018, 23:56
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Difficulty:

15% (low)

Question Stats:

88% (00:54) correct 12% (01:24) wrong based on 22 sessions

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If the circumference of a circle is 2x, what is the area of the circle in terms of x?

A. $$4\pi x^2$$

B. $$2\pi x^2$$

C. $$\pi x^2$$

D. $$\frac{x^2}{\pi}$$

E. $$\frac{x^2}{2\pi}$$

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Re: If the circumference of a circle is 2x, what is the area of the circle  [#permalink]

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06 Sep 2018, 02:17
Bunuel wrote:
If the circumference of a circle is 2x, what is the area of the circle in terms of x?

A. $$4\pi x^2$$

B. $$2\pi x^2$$

C. $$\pi x^2$$

D. $$\frac{x^2}{\pi}$$

E. $$\frac{x^2}{2\pi}$$

Circumference of Circle = 2πr (where r is the radius of circle)

Given, 2πr = 2x

i.e. Radius of circle, r = x/π

Area of circle = $$πr^2 = π(x/π)^2 = x^2/π$$

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Re: If the circumference of a circle is 2x, what is the area of the circle  [#permalink]

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06 Sep 2018, 07:00
Bunuel wrote:
If the circumference of a circle is 2x, what is the area of the circle in terms of x?

A. $$4\pi x^2$$

B. $$2\pi x^2$$

C. $$\pi x^2$$

D. $$\frac{x^2}{\pi}$$

E. $$\frac{x^2}{2\pi}$$

$$2πr = 2x$$

So, $$πr = x$$

Or, $$r = \frac{x}{π}$$

Thus, Area of the circle in terms of $$x$$ is $$π*\frac{x}{π}*\frac{x}{π} = \frac{x^2}{π}$$ , Answer must be (D)
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Re: If the circumference of a circle is 2x, what is the area of the circle   [#permalink] 06 Sep 2018, 07:00
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