Question

find the area of the blue shaded region. round to the nearest tenth.

Explanation:

Step1: Calculate the area of the whole circle

The formula for the area of a circle is \(A = \pi r^{2}\), where \(r = 5\) cm.
\(A_{circle}=\pi\times5^{2}=25\pi\) \(cm^{2}\)

Step2: Calculate the area of the un - shaded sector

The formula for the area of a sector is \(A=\frac{\theta}{360}\times\pi r^{2}\), where \(\theta = 60^{\circ}\) and \(r = 5\) cm.
\(A_{sector}=\frac{60}{360}\times\pi\times5^{2}=\frac{1}{6}\times25\pi=\frac{25\pi}{6}\) \(cm^{2}\)

Step3: Calculate the area of the shaded region

\(A_{shaded}=A_{circle}-A_{sector}\)
\(A_{shaded}=25\pi-\frac{25\pi}{6}=\frac{150\pi - 25\pi}{6}=\frac{125\pi}{6}\)
Substitute \(\pi\approx3.14\)
\(A_{shaded}=\frac{125\times3.14}{6}=\frac{392.5}{6}\approx65.4\) \(cm^{2}\)

Answer:

\(65.4\) \(cm^{2}\)