Question

in the diagram of a circle shown below:

• point g is the center of the circle.
• the radius of the circle measures 12.2 inches.
• ( mangle hgj = 98^{circ} )

what is the area, to the nearest tenth of a square inch of the shaded sector? use 3.14 for ( pi ).

127.3 in²
55.8 in²
27.9 in²
340.1 in²

Explanation:

Step1: Recall the formula for the area of a sector

The formula for the area of a sector of a circle is \( A=\frac{\theta}{360}\times\pi r^{2}\), where \(\theta\) is the central angle and \(r\) is the radius.

Step2: Identify the values of \(\theta\) and \(r\)

We are given that \(r = 12.2\) inches and \(\theta=360 - 98=262^{\circ}\), and \(\pi = 3.14\).

Step3: Substitute the values into the formula

$$
LATEXBLOCK0
$$

First, calculate \(3.14\times148.84 = 467.3576\). Then, \(\frac{262}{360}\times467.3576\approx\frac{262\times467.3576}{360}\)
\(262\times467.3576 = 122447.6912\), and \(\frac{122447.6912}{360}\approx340.1\)

Answer:

\(340.1\ \text{in}^{2}\) (the fourth option)