Figure not drawn to scale.In the circle above, the length of AO is 1, and x = 88º. What is the area of sector AOB? A) π B) 11π C) 5π D) 11/45π
Accepted Solution
A:
Though you do not provide a diagram, I am going to give this a try by assuming that O is the center of the circle, OA is a radius, and angle AOB is a central angle that measures 88 degrees.
We want to find out the area of sector AOB. First, we need to find the area of the entire circle. The area of a circle is given by [tex]A= \pi r^{2} [/tex] and since the radius of this circle is equal to 1, the area is [tex] \pi ( 1^{2} )= \pi [/tex]
Next we need to know what fraction of the circle sector AOB represents. The distance around the circle is 360 degrees but the central angle that intercepts arc AB is 88 degrees. That meas that the fraction of the circle the sector represents is given by [tex] \frac{88}{360}= \frac{11}{45} [/tex]
We multiply this by the area to obtain [tex] \frac{11}{45} \pi [/tex] which is the area of the sector.