A board is cut from a cylindrical log as shown in the
cross section below. If the cant size is 8.3 inches and the log diameter is
15.8 inches , find the largest thickness, *x*, of a board of width 10.0 inches
that can be cut on the side.

Solution:

Draw two construction lines from the centre of the log, to form right triangle ABC.

In triangle ABC;

AB = radius of log 15.8/2=7.9 inches

BC = (board width)/2=10.0/2=5.0 inches

Using the Theorem of Pythagorus,

AC2 = AB2 - BC2=7.92-5.02, and AC is approximately 6.12 inches

Now, AD = (cant size)/2 = 8.3 inches /2 = 4.15 inches

therefore *x* = DC = AC - AD = 6.12 inches - 4.15 inches = 1.97 inches

And so the largest thickness of a board of width 10.0 inches that can be cut on the side is approximately 2.0 inches.

Note that since no allowance has been made in this solution for loss of dimension due to saw kerf, the thickness of the side board will be overstated.