Answer:
3.3 units²
Step-by-step explanation:
Hi there!
[tex]\frac{Angle(sector)}{360} = \frac{Area (sector)}{Area (circle)}[/tex]
Angle of the sector: 15 degrees
Area of the sector: solving for
Area of the circle: ?
1) Determine the area of the circle
[tex]A=\pi r^2[/tex] where r is the radius
Plug in the radius (5)
[tex]A=\pi (5)^2\\A=25\pi[/tex]
Therefore, the area of the circle is 25π units².
2) Plug all information into sector formula
[tex]\frac{Angle(sector)}{360} = \frac{Area (sector)}{Area (circle)}\\\frac{15}{360} = \frac{Area (sector)}{25\pi }[/tex]
Multiply both sides by 25π
[tex]\frac{15}{360} *25\pi = Area(sector)\\\frac{15}{360} *25\pi = Area(sector)\\3.3=Area(sector)[/tex]
Therefore, the area of the sector is approximately 3.3 units².
I hope this helps!
