board foot

Problem 38
A log 18 ft. long is 2 ft. in diameter at the top end and 3 ft. in diameter at the butt end.
 

1. How many cubic feet of wood does the log contain?
2. How many cubic feet are there in the largest piece of timber of square cross section that can be cut from the log?
3. How many cubic feet are in the largest piece of square timber of the same size throughout its whole length?
4. How many board feet does the piece of timber in (c), a board foot being equivalent to a board 1 ft. square and 1 in. thick?

Hint: In (b) the larger end is the square ABCD. What is the smaller end? In (c) one end is the square EFGH. What is the other end?

Problem 2
Compute the cost of lumber necessary to resurface a footbridge 16 ft. wide and 150 ft. long with 2-in. planks, if lumber is \$40 per 1000 board feet. Neglect waste. (One board foot = 1 ft. by 1 ft. by 1 in.)