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Which of the following expresses the area of a circle in ter

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Which of the following expresses the area of a circle in ter [#permalink]  16 May 2017, 07:45
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Which of the following expresses the area of a circle in terms of C its circumference?

A) \frac{C^2}{4 pi}

B) \frac{C^2}{2 pi}

C) \frac{C}{2 pi}

D) \frac{C pi}{4}

E) \frac{C}{4 pi}

pi= π
[Reveal] Spoiler: OA

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Re: Which of the following expresses the area of a circle in ter [#permalink]  09 Oct 2017, 07:54
The circumference of a circle is computed as C = 2\pi r, while the area of a circle is A =\pi r^2.

Looking at the choices, it is easy to notice that there is no r in them. This means we have to substitute for r into the formula of the area.

In other words, from the circumference formula we get r= \frac{C}{2pi}, which can be used to substitute into the area formula A =\pi (\frac{C}{2pi})^2 = \pi\frac{C^2}{4pi^2} = \frac{C^2}{4pi}.

Re: Which of the following expresses the area of a circle in ter   [#permalink] 09 Oct 2017, 07:54
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Which of the following expresses the area of a circle in ter

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