Two circles have circumferences of π and 3π. What is the ratio

of the area of the circles? the diameters? the radii?

diam ratio = 3

area ratio = 3^2

To find the ratio of the areas of the circles, we first need to calculate the areas of the circles using the given circumferences. The formula to find the area of a circle is A = πr², where A is the area and r is the radius of the circle.

Let's calculate the areas of the circles:
Circle 1:
Circumference = π
C = 2πr (circumference formula)
π = 2πr (given circumference)
r = 1 (divide both sides by 2π to solve for the radius)

Area of Circle 1:
A1 = π(1)² = π

Circle 2:
Circumference = 3π
C = 2πr (circumference formula)
3π = 2πr (given circumference)
r = 3/2 (divide both sides by 2π to solve for the radius)

Area of Circle 2:
A2 = π(3/2)² = 9π/4

Now, we can find the ratio of the areas by dividing the area of Circle 2 by the area of Circle 1:

Ratio of areas = A2/A1 = (9π/4) / π = 9/4

So, the ratio of the areas of the circles is 9/4.

To determine the ratio of the diameters, we need to calculate the diameters of each circle. The diameter of a circle is twice its radius.

Let's calculate the diameters:
Diameter of Circle 1:
d1 = 2r1 = 2(1) = 2

Diameter of Circle 2:
d2 = 2r2 = 2(3/2) = 3

Now, we can find the ratio of the diameters by dividing the diameter of Circle 2 by the diameter of Circle 1:

Ratio of diameters = d2/d1 = 3/2

So, the ratio of the diameters of the circles is 3/2.

Finally, to find the ratio of the radii, we divide the radius of Circle 2 by the radius of Circle 1:

Ratio of radii = r2/r1 = (3/2)/1 = 3/2

So, the ratio of the radii of the circles is 3/2.