A circle can be cut into smaller and smaller slices and rearranged in the shape of a parallelogram as shown. The formula for finding the area, A, of a parallelogram with base b and height h is shown. Which equation represents the circumference of a circle in terms of its area?
To find the circumference of a circle, we use the formula \(C = 2\pi r\), where \(r\) is the radius of the circle.
Given that the area of a circle is \(A = \pi r^2\), we can solve for the radius in terms of the area:
\[r = \sqrt{\frac{A}{\pi}}\]
Plugging this value for the radius back into the circumference formula, we get:
\[C = 2\pi \sqrt{\frac{A}{\pi}}\]
Therefore, the equation representing the circumference of a circle in terms of its area is:
\[C = 2\sqrt{\pi A}\]