Question

given circles w and x below. find the area of the shaded region. round your answer to the nearest tenth if necessary.

Explanation:

Step1: Find the radius of each circle

The formula for the area of a circle is \(A = \pi r^{2}\), where \(r\) is the radius.
For circle \(X\), the diameter \(d = 30\), so the radius \(r_{X}=\frac{d}{2}=15\).
For circle \(W\), the radius \(r_{W}\) is twice the radius of circle \(X\) (since the diameter of \(X\) is the radius of \(W\)), so \(r_{W}=30\).

Step2: Calculate the area of each circle

The area of circle \(X\) is \(A_{X}=\pi r_{X}^{2}=\pi\times15^{2}=225\pi\).
The area of circle \(W\) is \(A_{W}=\pi r_{W}^{2}=\pi\times30^{2}=900\pi\).

Step3: Find the area of the shaded region

The area of the shaded region \(A = A_{W}-A_{X}\).
Substitute the values: \(A = 900\pi - 225\pi=675\pi\).
Using \(\pi\approx3.14\), we get \(A\approx675\times3.14 = 2119.5\).

Answer:

\(2119.5\)