Question

The circumference of Circle K is π. The circumference of Circle L is 4 π.

a. What is the ratio of their circumferences? of their radii? of their areas?

b. What do you notice?

Answer 1

a. What is the ratio of their circumferences? of their radii? of their areas?
C = 2πr
C1 = π and C2 = 4π
C1 / C2 = π / 4π = 1/4

C1 / C2 = 1/4 = 2πr1 / 2πr2
r1/r2 = 1/4

A = πr^2
A1 / A2 = π(r1)^2 / π(r2)^2
A1 / A2 = (r1/r2)^2 = (1/4)^2 = 1/16

b. What do you notice?
The ratio of the areas is the square of the ratio of the radii and the ratio of the circumference is equal to that of the radii.