Answer :
To find the area of a sector, we can use the formula for the area of a sector of a circle, which is:
[tex]A = \frac{\theta}{360} \times \pi \times r^2[/tex]
where:
- [tex]A[/tex] is the area of the sector,
- [tex]\theta[/tex] is the central angle of the sector in degrees,
- [tex]r[/tex] is the radius of the circle.
In this problem, we are given that the central angle [tex]\theta = 221[/tex] degrees, and the radius [tex]r = 5[/tex] feet. Let's calculate the area.
- Plug the values into the formula:
[tex]A = \frac{221}{360} \times \pi \times (5)^2[/tex]
- Calculate the fraction of the circle represented by the angle:
[tex]\frac{221}{360} \approx 0.61389[/tex]
- Square the radius:
[tex]5^2 = 25[/tex]
- Plug these into the formula:
[tex]A = 0.61389 \times \pi \times 25[/tex]
- Calculate [tex]A[/tex]:
[tex]A \approx 0.61389 \times 3.14159 \times 25[/tex]
[tex]A \approx 48.285 \, \text{square feet}[/tex]
Thus, the area of the larger sector is approximately [tex]48.285[/tex] square feet.
