Multiple choice

If the area of a circle is $A$, radius of the circle is $r$ and circumference of it is $C$, then

  1. $rC = 2A$
  2. $\displaystyle \frac{C}{A}=\frac{r}{2}$
  3. $\displaystyle AC=\frac{r^{2}}{4}$
  4. $\displaystyle \frac{A}{r}=C$
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A Correct answer
Explanation

Area A = pi*r^2 and Circumference C = 2*pi*r. Thus, r*C = r*(2*pi*r) = 2*pi*r^2 = 2*A.

AI explanation

Using the standard formulas for a circle, the area A equals pi times r squared and the circumference C equals 2 times pi times r. By multiplying the radius by the circumference, you get r multiplied by 2 times pi times r, which simplifies to 2 times pi times r squared. Replacing pi times r squared with A demonstrates that r times C equals 2A.

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