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

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?

The obvious answer is that he dunked it into a bath full of water and measured the runoff.

Dudeneys' answer is similar but more unwieldy:

The man made a box $3$ feet by $1$ foot by $1$ foot inside,

and into this he placed the pedestal.

Then he filled the box with fine dry sand, shaking it down and levelling the top.

Then he took out the pedestal, and the sand was shaken down and levelled,

when the surface was found to be exactly $2$ feet from the top of the box.

And so on.