If the diameter of circle C is 3 times greater than the diameter of circle D, how many times greater is the area of circle C compared to circle D?

To find out how many times the area of circle C is compared to circle D, we need to use the formula for the area of a circle, which is A = πr², where r is the radius of the circle.

First, let’s denote the diameter of circle D as d. Therefore, the radius of circle D would be r_d = d/2.

Given that the diameter of circle C is 3 times the diameter of circle D, the diameter of circle C would be 3d. Thus, the radius of circle C is r_c = 3d/2.

Now, we can calculate the area of both circles:

• Area of circle D: A_d = π(r_d)² = π(d/2)² = π(d²/4) = (π/4)d²
• Area of circle C: A_c = π(r_c)² = π(3d/2)² = π(9d²/4) = (9π/4)d²

To find out how many times the area of circle C is compared to circle D, we divide the area of circle C by the area of circle D:

Ratio = A_c / A_d = ((9π/4)d²) / ((π/4)d²) = 9

This means the area of circle C is 9 times the area of circle D.