The area of the ring bounded by two concentric circles is 175pi, and the radius of the smaller

The area of the ring bounded by two concentric circles is 175pi, and the radius of the smaller circle is 15, find the radius of the larger circle.

Let’s say that our ring is bounded by two circles, the radius of the larger of which is equal to R, and the radius of the smaller one is equal to r.

The area of a circle with radius r is S = π * r², and the area of a circle with radius R is S = π * R².

The area of the ring will be equal to the difference between the areas of the indicated circles:

s = π * R² – π * r².

By the condition of the problem, this area is 175 * π, and r = 15.

Substitute these values into our expression for the area of the ring:

175 * π = π * R ² – π * 15²,

175 = R² – 225,

R² = 175 + 225,

R² = 400,

R = 20.