Given a circle with radius $8$ units and a central angle $\theta$ measuring $\frac{2}{3}$ radians, what is the area of the shaded sector?

• A. $256$
• B. $85$
• C. $96$
• D. $32$

Answer: (D)

Verified step by step guidance

1. Identify the given values: the radius of the circle \(r = 8\) units and the central angle \(\theta = \frac{2}{3}\) radians.
2. 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.
3. Substitute the given values into the formula: \(\text{Area} = \frac{1}{2} \times 8^{2} \times \frac{2}{3}\).
4. Simplify the expression step-by-step: first calculate \$8^{2}\(, then multiply by \)\frac{1}{2}\( and \)\frac{2}{3}$ accordingly.
5. The result after simplification will give the area of the shaded sector in square units.