![[diagram]](balloon.gif)
cm long lies as straight as possible on the surface of a spherical balloon while it is being inflated. The balloon remains spherical at all times, and the hair, which doesn't stretch or shrink, remains as straight as possible on its surface.
a. How is the radius of the balloon changing when it is 4 cm, if the ends of the hair are moving apart at 1 cm/s at that instant? [4]
b. At the same instant, how quickly is the midpoint of the hair aproaching the line between the two ends? [4]
2. Suppose that two squares are cut off diagonally opposite corners of a standard 8 
8 chessboard.
![[mutilated chessboard]](chessboard.gif)
If you are given 31 dominoes, each of which is just the right size to cover two adjacent squares of the board, can you place them so that all 62 remaining squares of the board are covered? You should either show how this can be done or prove that it cannot be done. [2]
Department of Mathematics
Trent University