two concentric circle with the ratio of radii as 2:3, what is the ratio of the circumferences
also 2:3
To find the ratio of the circumferences of two concentric circles with a ratio of radii, you need to understand the relationship between the circumference and the radius of a circle.
The formula for the circumference of a circle is C = 2πr, where C represents the circumference and r represents the radius. In this case, let's assume the radius of the smaller circle is r1 and the radius of the larger circle is r2.
Given the ratio of the radii as 2:3, we can express them in terms of each other. Let r1 = 2x and r2 = 3x, where x is a constant factor.
Now, substitute these values into the circumference formula for both circles:
C1 = 2πr1 = 2π(2x) = 4πx
C2 = 2πr2 = 2π(3x) = 6πx
Therefore, the ratio of the circumferences (C2/C1) can be calculated as:
(C2/C1) = (6πx)/(4πx) = 3/2
Hence, the ratio of the circumferences of two concentric circles with a ratio of radii of 2:3 is 3:2.