What is the area of the sector of a circle with central angle (5pi)/2 ...?

2 Answers
Jun 6, 2018

If we assume that the angle stated is (5pi)/2 (and not 5pi/2), then we can see that it is equal to pi/2, which is 1/4 of a circle, and the area of the sector, then, is: (pir^2)/4

Explanation:

I am assuming that you meant the central angle to be (5pi)/2 and not 5pi/2.
If this is the wrong assumption, please let me know.

The first issue with this angle of (5pi)/2 is that it goes beyond a full circle. A full circle has an angle of 2pi.
In fact, that angle (5pi)/2 is equivalent to a full circle ((4pi)/2) and then another pi/2 .

So, I interpret the area of interest here to be delimited by that angle of pi/2, which is 1/4 of a full circle. The area of a whole circle is: A_c=pir^2
Hence, the area of the sector, is A_s=(pir^2)*(1/4)=(pir^2)/4

Jun 6, 2018

The philosophical issue is whether a sector bigger than 2pi has an area bigger than the area of the circle. I'm going to say it does, so the area is

A= (theta/{2pi}) pi r^2 ={theta r^2}/2 = {5pi r^2}/4