Question

question 17 of 25
to the nearest square inch, what is the area of the shaded sector in the circle shown below?

a. 116 in²
b. 464 in²
c. 314 in²
d. 23 in²

Explanation:

Step1: Find full circle area

$$A_{circle} = \pi r^2 = \pi (10)^2 = 100\pi$$

Step2: Calculate sector fraction

$$\text{Fraction} = \frac{133^\circ}{360^\circ}$$

Step3: Compute sector area

$$A_{sector} = 100\pi \times \frac{133}{360} \approx 100 \times 3.1416 \times 0.3694 \approx 116$$

Answer:

A. 116 in²