Question

circle a has a radius of 6 meters. what is the area of the shaded sector in square meters? options: \\(\frac{5}{6}\pi\\), \\(\frac{5}{3}\pi\\), \\(5\pi\\), \\(300\pi\\)

Explanation:

Step1: Recall the formula for the area of a sector

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

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

Here, the radius \( r = 6 \) meters and the central angle \( \theta=50^{\circ} \).

Step3: Substitute the values into the formula

First, calculate \( r^{2}=6^{2} = 36 \). Then, substitute into the sector area formula:
\( A=\frac{50}{360}\times\pi\times36 \)
Simplify \( \frac{50}{360}\times36 \): \( \frac{50\times36}{360}=\frac{50}{10} = 5 \). So the area \( A = 5\pi \).

Answer:

\( 5\pi \)