The length of the arc formed inside a circle and the area of the sector depends on the radius and central angle formed inside the circle.
Part A: The length of the arc is 5.652 m.
Part B: The area of the sector is 62.8 square feet.
What is the area of the sector inside a circle?
A circle sector is the portion of a circle that is enclosed by two radii and an arc, where the smaller area is known as the minor sector and the larger being the major sector.
Part A:
Given that the radius r of the circle is 5.4 m and the central angle is 60 degrees.
The length of the arc is calculated as given below.
[tex]s = r\theta[/tex]
Where s is the length of the arc, and [tex]\theta[/tex] is the central angle.
[tex]s = 5.4 \times 60 \times \dfrac {\pi}{180} \;\rm radians[/tex]
[tex]s = 5.652 \;\rm m[/tex]
Hence we can conclude that the length of the arc is 5.652 m.
Part B:
Given that the radius r of the circle is 4 ft. and the central angle is 5π/2 degrees.
The area of the sector is calculated as given below.
[tex]A = \dfrac {\theta}{2\pi}\times \pi r^2[/tex]
Where A is the area of the sector, and [tex]\theta[/tex] is the central angle.
[tex]A = \dfrac {5\pi}{2} \times \dfrac {1}{2\pi} \times \pi 4^2[/tex]
[tex]A = \dfrac {5}{4} \times \pi \times 16[/tex]
[tex]A = 62.8 \;\rm ft^2[/tex]
Hence we can conclude that the area of the sector is 62.8 square feet.
To know more about the area of the sector, follow the link given below.
https://brainly.com/question/1582027.
