Question

This design shows several circles with the same center. The total radius of the design is 8 inches. The angle shown has a measure of 30°. The shaded section of the outermost ring has a side length of 2 in. What is the perimeter of the shaded portion? Express the answer as a decimal rounded to the nearest hundredth.

Answer 1

11.33 in. to the nearest hundredth.

Explanation:

The perimeter of the shaded area = length of the 2 straight lines + the length of the 2 arcs = 4 + length of the 2 arcs.

Calculate the length of the outer arc:

This equals (30 / 360) * perimeter of the largest circle

= 1/12 * 2 π * 8

= 4/3 π in.

The inner circle has a radius of 8 - 2 = 6 ins

so the length of the inner arc

= 1/12 * π * 2 * 6

= π in.

So the perimeter of the shaded region = 4 + 4/3 π + π

= 4 + 7π/3

= 11.33 in.