Uses of π
In high school geometry, we learn yet another use of π. We learn to take the area of a part of a circle. The formula for this is:
This is where K is equal to the area of the sector and n is equal to the angle measured in degrees of the sector. This is essentially just our area formula divided by the portion of our circle. So, try this for size:
A circle with a radius of 5 has a sector of 37 degrees. What is the area of the sector?
Take what we know (r = 5 and n = 37) and plug it into our formula:
Do the math and you end up with K=2.57 π or approximately 8.07
Along the same lines, we can find the length of that arc (a.k.a. the circumference of the arc) Take the formula:
As you can see, this is the circumference formula using n/360 to get a proportion of the original circle's circumference.