To determine how many times greater the area of circle C is compared to circle D, we first need to understand the relationship between the diameters and the areas of the circles.
Let’s define the diameter of circle D as d. This means the diameter of circle C, which is stated to be 3 times greater than that of circle D, will be:
Diameter of circle C = 3d
The formula for the area A of a circle is given by:
A = πr²
Where r is the radius of the circle. The radius is half of the diameter, so we have:
Radius of circle D, rD = d/2
Radius of circle C, rC = (3d)/2
Next, we can calculate the areas of both circles:
Area of circle D:
AD = π(rD)² = π(d/2)² = π(d²/4)
Area of circle C:
AC = π(rC)² = π((3d)/2)² = π(9d²/4)
Now, we can find the ratio of the areas of circle C to circle D:
Ratio = AC / AD = (π(9d²/4)) / (π(d²/4))
The π and (d²/4) terms cancel out, leading to:
Ratio = 9
This means that the area of circle C is 9 times greater than the area of circle D.