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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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Question Stats:

81% (00:32) correct 18% (00:28) wrong based on 33 sessions

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) $$\frac{C}{4\pi}$$
[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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