Could you help me with this math question please?

Sly_Si
Mon, 26 May 2008 06:58:55 +0000

For those who are getting 6+18/r, that IS an answer choice; it’s equal to (6r+18)/r, which is E.

Here’s another way to think about the problem. This is how I would check my answer if I were doing this on a test:
When r is very large, the sector that cuts off an arc length of 6 becomes very small. A arc of a circle subtending a very small angle is almost a straight line. So that region outside the circle (bounded by segments of length 3 and arcs of length 6 and x) is almost rectangular. Thus x must be very close to 6 as r becomes very large. The only answer choice that behaves like that is E.