Question

If the circumference of circle I is equal to the diameter of circle II, what is the ratio of the area of circle II to the area of circle I?

Answer 1

Since C=pi d, the diameter and radius of circle II is larger than circle I by a factor of pi. That means the areas will vary by a factor of pi squared, since the radius of the larger circle will be squared when calculating the area. If r is the radius of the circle I,\[A_1=\pi r^2\]\[A_2=\pi (r \pi)^2=\pi ^2A_1\]