Question

the shaded area in the circle below represents a damaged section of a 6 - foot - diameter sidewalk.
what is closest to the area of the damaged section?
○ 6.0 square feet
○ 8.1 square feet
○ 4.0 square feet
○ 7.7 square feet

Explanation:

Step1: Find circle radius

The diameter is 6 feet, so radius $r = \frac{6}{2} = 3$ feet.

Step2: Estimate sector angle

The damaged sector is a 90° (right angle) sector, so $\theta = 90^\circ$.

Step3: Calculate sector area

Use sector area formula $A = \frac{\theta}{360^\circ} \times \pi r^2$.
Substitute values: $A = \frac{90^\circ}{360^\circ} \times \pi \times 3^2 = \frac{1}{4} \times \pi \times 9 = \frac{9\pi}{4} \approx 7.07$ square feet.

Step4: Match to closest option

7.07 is closest to 7.7 square feet.

Answer:

7.7 square feet