2/28/11

Test 3 Section 2 - #17 (page 518)

This question can be GUESSTIMATED, since the diagram is drawn to scale. Note that AD = 6, so the radius of the circle is 3, which means the area of the circle is 9π.

Now look at the answer choices. We're looking for the area of the shaded region, which has to be smaller than 9π. Cross off (D) and (E) right away.

We're not done guesstimating yet, though. Take your hand and cover up the top half of the circle, so you're only looking at the bottom half (or the top half...they're the same). I think it's easier to tell with half the circle covered that most of the circle is shaded. Look at your answer choices again. Half of the circle would be 4.5π. That makes me very comfortable crossing off (A) (which is less than half the circle) and pretty comfortable crossing off (B), which is not much more than half the circle. (C) is 2/3 of the circle, which looks about right to me. I choose (C).

Note that, of course, there is a mathematical solution to this problem as well, but it's not necessary if you're a good guesstimater. It basically comes down to 9π - 4π + π, though. See if you can see where those numbers come from.