The radius of one circle is 4 times the radius of the other, and the length of the circle itself is 15 cm

The radius of one circle is 4 times the radius of the other, and the length of the circle itself is 15 cm larger. Find the radii of each circle.

Let’s denote the radius of the smaller circle as x.

Then the radius of the larger circle is 4x.

The length of the smaller circle is 2πх, the length of the larger circle
2π * 4x = 8πx.

The difference in the lengths of these circles is 15 cm, we compose and solve the equation:

8πx – 2πx = 15;

6πx = 15;

x = 5 / (2π) = 5 / (2 * 3.14) ≈ 0.8 (cm).

So, the radius of the smaller circle is 0.8 cm, the radius of the larger circle is 0.8 * 4 = 3.2 cm.

Answer: 0.8 cm and 3.2 cm.