Thread: Sector area and probability questions

Hello. For the first question refer to this:

http://img693.imageshack.us/img693/8362/46035151.jpg - the outer numbers are degrees

What I want to do is find the area in the middle there (where the two and arrows are). Not quite sure how to go about it though. I was thinking divide the sections into triangle but I'd need a radius. Anyway the answer is .


Second question: "A dart is thrown at a board 12m long and 5m wide. Attached to the board are 30 balloons, each with radius 10cm. Assuming each balloon lies entirely on the board, find the probability that a dart that hits the board will also hit a balloon."

I'm not even sure where to start here.

The answer is pi/200 is about 0.016.

Basically I just want to see how each was worked out. Thanks.

Hello, Phil!

Find the area of the middle region.

Answer: .

Code:

              * * *
          *           *
      A ♥ - - - + - - - ♥ B
       *  *     |     *  *
            *   |1  *
      *       * | *       *
      *         ♥O        *
      *       * | *       *
            *   |1  *
       *  *     |     *  *
        * - - - + - - - *
          *           *
              * * *

Note all the angles.

We find that the radius is 2.
The area of the circle is: .


The area of sector is: .

The area of

The area of the segment is: .


The area of the middle region is: .

. .

Thank you - was very helpful.