Answer:
87.5π units.
Step-by-step explanation:
First off, you need to find the area of the entire circle.
The formula for that is πr^2. In this case, it is π * 15^2, which is 225π.
Then, you can set up a proportion to find the area of the shaded sector.
[tex]\frac{x}{140} =\frac{225\pi }{360}[/tex]
This means that the area of the sector over the degrees of the angle equals the area of the circle over the degrees of the circle.
That results in...
360x = 140 * 225π
360x = 31500π
36x = 3150π
x = 87.5π
And that's your area!
Hope this helps!
