Question

ring - shaped region is shown below. its inner radius is 6 in, and its outer radius is 9 in. find the area of the shaded region. use 3.14 for π. do not round your answer.

Explanation:

Step1: Calculate the area of the outer circle

The formula for the area of a circle is \(A = \pi r^{2}\). For the outer circle with radius \(r_{1}=9\) in, \(A_{1}=\pi r_{1}^{2}=3.14\times9^{2}=3.14\times81\).

Step2: Calculate the area of the inner circle

For the inner circle with radius \(r_{2} = 6\) in, \(A_{2}=\pi r_{2}^{2}=3.14\times6^{2}=3.14\times36\).

Step3: Find the area of the shaded region

The area of the shaded region (annulus) is \(A = A_{1}-A_{2}\). Substitute \(A_{1}\) and \(A_{2}\): \(A=3.14\times(81 - 36)=3.14\times45\).

Answer:

\(141.3\)