fabxx

There's a graph to this question. Can also help me out? I don't get why its 18pi, shouldn't it be 36pi?

C=36pi, and C=2rpi so therefore r=18. It's asking for the length of the curved path from A to B right? The curved path from A to B equals AO+OB, so it should be r+r=36pi. Why is it 18pi?

Thanks in advance. (You'll need to see the graph on the book to get what i'm saying)

nd09

the radius of each smaller circle is 9, so the total circumference of each smaller on is 2(9)pi = 18pi. However each is a semi circle or 9pi each, so 9pi + 9pi = 18pi

nguyenminhhieuh

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!

nguyenminhhieuh

btw, the solution nd09 offers is great ^^

fabxx

Thanks!!! XD