Question

1. when ba = 10 ft, find the area of the region that is not shaded. round to the nearest whole number. 305 ft² 262 ft² 43 ft² 52 ft²

Explanation:

Step1: Find circle area

Area of circle: $A = \pi r^2 = \pi (10)^2 = 100\pi \approx 314.16$ ft²

Step2: Find shaded sector area

Sector area: $A_{sector} = \frac{60}{360} \times 100\pi = \frac{100\pi}{6} \approx 52.36$ ft²

Step3: Calculate unshaded area

Unshaded area = Circle area - Sector area $\approx 314.16 - 52.36 = 261.8 \approx 262$ ft² (Note: Correction—original answer option 262 is correct; likely miscalculation earlier. Correct unshaded area is ~262 ft².)

Step1: Compute circle area

$A = \pi (10)^2 = 100\pi \approx 314.16$ ft²

Step2: Compute shaded sector area

$A_{sector} = \frac{60}{360} \times 314.16 \approx 52.36$ ft²

Step3: Find unshaded area

Unshaded = $314.16 - 52.36 \approx 262$ ft²

Answer:

305 ft²