If the measure of central angle $ABC$ in a circle of radius $6$ units is $\frac{1}{2}$ radians, what is the area of the shaded sector?

• A. $6$
• B. $36$
• C. $18$
• D. $9$

Answer: (C)

Verified step by step guidance

1. Identify the given values: the radius of the circle \(r = 6\) units and the central angle \(\theta = \frac{1}{2}\) 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: \(\text{Area} = \frac{1}{2} \times 6^{2} \times \frac{1}{2}\).
4. Simplify the expression step-by-step: first calculate \$6^{2}\(, then multiply by \)\frac{1}{2}\(, and finally multiply by \)\frac{1}{2}$ again.
5. The result after simplification will give the area of the shaded sector in square units.