Question

question 7
1 pts
find the approximate area of the shaded sector. use 3.14 for pi. round your answer to the nearest hundredth.
options: 177.51 in², 23.45 in², 22.19 in², 2.93 in²

Explanation:

Step1: Find the area of the whole circle

The formula for the area of a circle is \( A = \pi r^2 \), where \( r = 8 \) in and \( \pi \approx 3.14 \).
\( A = 3.14\times8^2 = 3.14\times64 = 200.96 \) \( \text{in}^2 \)

Step2: Find the fraction of the circle that is shaded

The unshaded sector has a central angle of \( 42^\circ \), so the shaded sector has a central angle of \( 360^\circ - 42^\circ = 318^\circ \).
The fraction of the circle that is shaded is \( \frac{318}{360} \)

Step3: Find the area of the shaded sector

Multiply the area of the whole circle by the fraction of the shaded sector.
\( \text{Shaded Area} = 200.96\times\frac{318}{360} \)
First, simplify \( \frac{318}{360} \approx 0.8833 \)
Then, \( 200.96\times0.8833 \approx 177.51 \) \( \text{in}^2 \)

Answer:

177.51 in²