The ratio of the radii of two circles is 2:3. Find the ratio of their circumference and the ratio of their areas
since C = 2piR
the ratio of circumferences is the same as the ratio of the radii.
That is, if we substitute kR for R, we get
2pi(kR) = k*2piR = kC
To find the ratio of the circumference of two circles, divide the circumference of the first circle by the circumference of the second circle.
The formula for the circumference of a circle is C = 2πr, where C is the circumference and r is the radius. Let's assume the radii of the two circles are r1 and r2, and it's given that their ratio is 2:3.
The ratio of their circumference (C1:C2) can be calculated as follows:
C1/C2 = (2πr1)/(2πr2) = r1/r2
Similarly, to find the ratio of the areas of two circles, divide the area of the first circle by the area of the second circle.
The formula for the area of a circle is A = πr^2. Again, assuming the radii are r1 and r2, the ratio of their areas (A1:A2) can be calculated as follows:
A1/A2 = (πr1^2)/(πr2^2) = (r1^2)/(r2^2)
Therefore, the ratio of their circumferences and the ratio of their areas are r1/r2 and (r1^2)/(r2^2), respectively.