For this problem, we are given two circles, M and N, that are related by a scale factor of 3, we know that the circumference of the larger circle is 6 cm, and we need to determine the circumference of the smaller one.
The circumference of a circle can be found by using the following expression:
[tex]C=2\pi r[/tex]
Where 'r' is the radius. When the circles are scaled, their radii should be scaled at the same proportion, so the following demonstrates the relation between both radii:
[tex]r_n=3\cdot r_m[/tex]
We know that the circumference for the circle N is equal to 6 cm, therefore we have:
[tex]6=2\pi\cdot r_n[/tex]
If we replace the radius for circle n, with the second expression, we will obtain:
[tex]\begin{gathered} 6=2\pi\cdot(3\cdot r_m) \\ 6=3\cdot(2\pi r_m) \\ \frac{6}{3}=C_m \\ C_m=2 \end{gathered}[/tex]
Circle M's circumference is equal to 2 cm.
