What is the area of the sector of a circle with θ=75° and a radius of 4 feet? Include pi in your calculation.(1 point)

Question

Responses

A=10.472 ft.2
upper A equals 10.472 ft. squared

A=50.265 ft.2
upper A equals 20.265 ft. squared

A=39.794 ft.2
upper A equals 39.794 ft. squared

A=2.168 ft.2
upper A equals 2.168 ft. squared

Answer 1

To find the area of the sector of a circle, you can use the formula:

\[ A = \frac{\theta}{360} \times \pi r^2 \]

where:

• \( A \) is the area of the sector,
• \( \theta \) is the angle in degrees,
• \( r \) is the radius of the circle.

Plugging in the values where \( \theta = 75^\circ \) and \( r = 4 \) feet:

\[ A = \frac{75}{360} \times \pi (4^2) \] \[ A = \frac{75}{360} \times \pi (16) \] \[ A = \frac{75 \times 16}{360} \times \pi \] \[ A = \frac{1200}{360} \times \pi \] \[ A = \frac{10}{3} \times \pi \] \[ A \approx 10.472 \pi \text{ ft}^2 \]

Thus, the area of the sector is approximately \( 10.472 \pi \) ft².

Looking at the provided options, the correct response is:

A = 10.472 ft²