OG Blue Book Math Page 398 #11

nguyenminhhieuh
Thu, 13 Nov 2008 22:56:52 +0000

Just another tricky solution: Moving the lower (OB) semi-circle upward to fit the upper (OA) semi-circle, you’ll see that these two semi-cirles compose a circle with diametre OA=1/2 AB = the length of the curved path we’re considering.
Since: circumference of larger circle (AB) = 2 Pi R
circumference of smaller circle (OA) = 2 Pi . 1/2 R = Pi R

====> curve A-B = 1/2 of 36 Pi = 18 Pi

My reasoning appears a lil verbose, but if you attack the problem this way, you’ll see how quick this solution is. In fact, it takes me fewer than 5 seconds to pick C as the answer!