Question

given circles d and e below. find the area of the shaded region. round your answer to the nearest tenth if necessary.
answer attempt 1 out of 2

Explanation:

Step1: Calculate the area of the larger circle

The formula for the area of a circle is \(A = \pi r^{2}\). The diameter of the smaller circle is \(4\), so the radius of the larger circle \(r_{D}=4\) (since the radius of the larger circle is equal to the diameter of the smaller circle). Then \(A_{D}=\pi\times4^{2}=16\pi\).

Step2: Calculate the area of the smaller circle

The radius of the smaller circle \(r_{E}=\frac{4}{2} = 2\). Using the area formula \(A=\pi r^{2}\), we get \(A_{E}=\pi\times2^{2}=4\pi\).

Step3: Calculate the area of the shaded region

The area of the shaded region \(A = A_{D}-A_{E}\). Substitute the values: \(A=16\pi - 4\pi=12\pi\approx12\times 3.14 = 37.7\).

Answer:

\(37.7\)