The lengths of the circles are equal to C = 48π, C2 = 32π. Find the width of the ring

Determine the radius of the larger circle.

C1 = 2 * π * R1.

R1 = C1 / 2 * π = 48 * π / 2 * π = 24 cm.

Determine the radius of the smaller circle.

C2 = 2 * π * R2.

R2 = C2 / 2 * π = 32 * π / 2 * π = 16 cm.

Let’s define the areas of the circles.

S1 = π * R1 ^ 2 = 576 * π cm2.

S2 = π * R2 ^ 2 = 256 * π cm2.

Then the area of the ring is equal to the difference between the areas of the circles.

S = S1 – S2 = 576 * π – 256 * π = 320 * π cm2.

Answer: The area of the ring is 320 * π cm2.