Question

1. if ( bd = 18 mathrm { cm } ), find the area of the shaded region in the circle.

Explanation:

Step1: Find the radius of the circle

Since \(BD = 18\) cm, the radius \(r=\frac{BD}{2}=\frac{18}{2}=9\) cm.

Step2: Find the central angle of the shaded region

The central angle of the un - shaded region adjacent to the \(136^{\circ}\) sector: \(\theta_1 = 180^{\circ}- 136^{\circ}=44^{\circ}\).
The central angle of the shaded region \(\theta=360^{\circ}-2\times44^{\circ}=272^{\circ}\).

Step3: Calculate the area of the shaded region

The area of a sector of a circle is given by \(A=\frac{\theta}{360}\times\pi r^{2}\).
Substitute \(\theta = 272^{\circ}\) and \(r = 9\) cm.
\(A=\frac{272}{360}\times\pi\times9^{2}\)
\(A=\frac{272}{360}\times\pi\times81\)
\(A=\frac{272\times81\pi}{360}\)
\(A=\frac{272\times9\pi}{40}\)
\(A=\frac{2448\pi}{40}=61.2\pi\)
Take \(\pi = 3.14\), then \(A=61.2\times3.14 = 192.168\) \(cm^{2}\)

Answer:

\(192.168\) \(cm^{2}\)