Question - Calculating Circumference of a Circle from Area

Solution:

The question asks for the circumference of a circle given its area. The area (A) of a circle is related to its radius (r) by the formula:\[ A = \pi r^2 \]Given that the area is 36π cm², we can set up the equation:\[ 36\pi = \pi r^2 \]We can solve for r by dividing both sides of the equation by π:\[ 36 = r^2 \]Taking the square root of both sides gives us:\[ r = \sqrt{36} \]\[ r = 6 \text{ cm} \]The circumference (C) of a circle is related to the radius by the formula:\[ C = 2\pi r \]Substituting the radius we found into the circumference formula gives us:\[ C = 2\pi \times 6 \]\[ C = 12\pi \]So the circumference of the circle is 12π centimeters.

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