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

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

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New post 06 Sep 2018, 00:56
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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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New post 06 Sep 2018, 03:17
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 = \(πr^2 = π(x/π)^2 = x^2/π\)

Answer: Option D
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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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New post 06 Sep 2018, 08:00
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 &nbs [#permalink] 06 Sep 2018, 08:00
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