Question

Find the area of the shaded region. RQ=71.5 inches and PO=93.4 inches. Use 3.14 for π as necessary.A. 18,468 in²B. 2,836 in²C. 25,886 in²D. 62,345 in²

Answer 1

We must find the area of the bigger circle and then the area of the smaller circle.

Area of the bigger circle:

Using the formula for the area, we have:

`\begin{gathered} A=\pi(PO)^2 \\ A=\pi(93.4)^2\text{ in}^2\text{(Replacing)} \\ A=27392\text{ in}^2\text{ (Raising the radius to the power of 2 and multiplying) } \end{gathered}`

Area of the smaller circle:

`\begin{gathered} _{}LO=PO-RQ\text{ (Finding the radius of the smaller circle)} \\ LO=(93.4-71.5)inches=21.9\text{ inches} \\ A=\pi(LO)^2\text{in}^2\text{ (Area of the smaller circle)} \\ A=\pi(21.9)^2\text{ in}^2\text{(Replacing)} \\ A=1506\text{in}^2\text{ (Raising the radius to the power of 2 and multiplying)} \\ \end{gathered}`

Area of the shaded region:

The area of the shaded region is: Ab - As (Ab:Area of the bigger circle, As: Area of the smaller circle)

The area of the shaded region is: (27392 - 1506) square inches = 25886 square inches.

The answer is the option C.