Henry Ernest Dudeney/Puzzles and Curious Problems/236 - The Pedestal Puzzle

by : $236$

 * The Pedestal Puzzle
 * A man had a block of wood measuring $3$ feet by $1$ foot by $1$ foot,
 * which he gave to a wood-turner with instructions to turn from it a pedestal,
 * saying that he would pay him a certain sum for every cubic inch of wood taken from the block in the process of turning.
 * The ingenious turner weighed the block and found it to contain $30$ pounds.
 * After he had finished the pedestal it was again weighed, and found to contain $20$ pounds.
 * As the original block contained $3$ cubic feet, and it had lost just one-third of its weight,
 * the turner asked payment for $1$ cubic foot.
 * But the gentleman objected, saying that the heart of the wood might be heavier or lighter than the outside.
 * How did the ingenious turned contrive to convince his customer that he had taken not more and not less than $1$ cubic foot from the block?