If the measure of central angle RST is $\theta$ radians in a circle of radius $r$, what is the area of the shaded sector if $r=4$ and $\theta =2$?

• A. $20$
• B. $16$
• C. $8$
• D. $4$

Answer: (C)

Verified step by step guidance

1. Recall the formula for the area of a sector of a circle: \(\text{Area} = \frac{1}{2} r^{2} \theta\), where \(r\) is the radius and \(\theta\) is the central angle in radians.
2. Identify the given values from the problem: radius \(r = 4\) and central angle \(\theta = 2\) radians.
3. Substitute the given values into the sector area formula: \(\text{Area} = \frac{1}{2} \times 4^{2} \times 2\).
4. Simplify the expression step-by-step: first calculate \$4^{2}\(, then multiply by \)2\(, and finally multiply by \)\frac{1}{2}$.
5. The result after simplification will give you the area of the shaded sector.