A circle is characterized by radius, arc, sectors and circumference
- The length of the major arc is [tex]18.75\pi[/tex]
- The radius of the circle is 15
- The area of the shaded sector is [tex]140.625 * \pi[/tex]
Length of the major arc
The given parameters are:
[tex]C = 30\pi[/tex] --- the circumference
[tex]\theta = 225^o[/tex] -- the center angle
The length of the major arc is calculated using:
[tex]L = \frac{\theta}{360} * C[/tex]
So, we have:
[tex]L = \frac{225}{360} *30\pi[/tex]
Evaluate
[tex]L = 18.75\pi[/tex]
Hence, the length of the major arc is [tex]18.75\pi[/tex]
The radius of the circle
The circumference is given as:
[tex]C = 30\pi[/tex]
So, we have:
[tex]2\pi r = 30\pi[/tex]
Divide through by 2pi
[tex]r = 15[/tex]
Hence, the radius of the circle is 15
The area of the shaded sector
The area of a sector is:
[tex]A = \frac{\theta}{360} * \pi r^2[/tex]
So, we have:
[tex]A = \frac{225}{360} * \pi * 15^2[/tex]
Evaluate
[tex]A = 140.625 * \pi[/tex]
Hence, the area of the shaded sector is [tex]140.625 * \pi[/tex]
Read more about circumference at:
https://brainly.com/question/15673093
