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

Puzzles and Curious Problems by Henry Ernest Dudeney: $236$

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?

1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Geometrical Problems: Various Geometrical Puzzles: $236$. -- The Pedestal Puzzle
1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Geometrical Problems: Solid Geometry Puzzles: $323$. The Pedestal Puzzle