Question

a ring - shaped region is shown below. its inner diameter is 22 m, and its outer diameter is 28 m. find the area of the shaded region. use 3.14 for π. do not round your answer.

Explanation:

Step1: Calculate the radius of the outer circle

The formula for radius \(r=\frac{d}{2}\), where \(d\) is the diameter.
For the outer circle, \(d = 28m\), so \(r_{outer}=\frac{28}{2}=14m\)

Step2: Calculate the radius of the inner circle

For the inner circle, \(d = 22m\), so \(r_{inner}=\frac{22}{2}=11m\)

Step3: Calculate the area of the outer circle

The formula for the area of a circle is \(A=\pi r^{2}\).
For the outer circle, \(A_{outer}=3.14\times14^{2}=3.14\times196 = 615.44m^{2}\)

Step4: Calculate the area of the inner circle

For the inner circle, \(A_{inner}=3.14\times11^{2}=3.14\times121=379.94m^{2}\)

Step5: Calculate the area of the shaded region

The area of the shaded region (ring - shaped) is \(A = A_{outer}-A_{inner}\)
\(A=615.44 - 379.94=235.5m^{2}\)

Answer:

\(235.5\)