Example Question - radius calculation

Calculating Circumference of a Circle from Area

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.