1. Calculate the area of various sectors of a circle.
2. Determine the probability of various events using sector area.
In earlier work, you learned to find the area of a circle. Sometimes we are not interested in the area of the entire circle but just in a portion of the circle known as a sector. A sector is a region of a circle that is bounded by a central angle and its intercepted arc. We can then use this area as a means to calculate geometric probability of an event such hitting the bullseye on a dartboard.
A brief description and two examples of how to find the area of a various sectors of a circle.
Find the area of a sector of a circle with radius 8 mm and bounded by a central angle measuring 150. (Yes, I know there's no sound).
Using measurements to find the probability of an event is known as geometric probability. Finding geometric probability using circles is fairly simple. For instance, the spinner shown here is divided into eight equal sections (despite what the image looks like). A typical question may ask what is the probability that a spinner would stop on the sector with the asterisk.
It should be fairly obvious that one of the eight even sections has an asterisk so the proability would be 1/8. If we prefer, we can change this fraction into a percentage. In this case, our proability would be 45%. In either case, we simply need to determine the ratio that the area of the sector (or portion of the circle) prepresents when compared to the area of the entire circle. In other words, simply create two "area" problems as a ratio.