What is the area of the sector of a circle with central angle 5π2...?

2 Answers
Jun 6, 2018

If we assume that the angle stated is 5π2 (and not 5π2), then we can see that it is equal to π2, which is 14 of a circle, and the area of the sector, then, is: πr24

Explanation:

I am assuming that you meant the central angle to be 5π2 and not 5π2.
If this is the wrong assumption, please let me know.

The first issue with this angle of 5π2 is that it goes beyond a full circle. A full circle has an angle of 2π.
In fact, that angle 5π2 is equivalent to a full circle (4π2) and then another π2 .

So, I interpret the area of interest here to be delimited by that angle of π2, which is 14 of a full circle. The area of a whole circle is: Ac=πr2
Hence, the area of the sector, is As=(πr2)(14)=πr24

Jun 6, 2018

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

A=(θ2π)πr2=θr22=5πr24