(a)
This step is not neccessarily, but for the sake of teaching
purposes, let us classify the wooden blocks cut out into three
groups, A, B and C. Note that the blocks in each individual group
are similar.
There is 1 block in Group A, which is the uppermost.
There are 2 blocks in Group B, which are the largest blocks.
There are 3 blocks in Group C, they are the remaining
blocks.
Total Volume of entire wooden structure
= 300cm X 150cm X 150cm = 6 750 000 cm^3
Volume of block in Group A
= 50cm X 50cm X 150cm
= 375 000 cm^3
Volume of blocks in Group B
= 2 X ( 30cm X 100cm X 150cm )
= 900 000 cm^3
Volume of blocks in Group C
= 3 X ( 100cm X 50cm X 30cm )
= 450 000 cm^3
Volume of Art Piece
= Volume of entire wooden structure - Volume of all the wooden
blocks
= 6 750 000 cm^3 - 375 000 cm^3 - 900 000 cm^3 - 450 000
cm^3
= 5 025 000 cm^3 = 5.025 m^3
(b)
Amount of dices that could be cut out from the block in Group
A
= 3 X 3 X 10 = 90 dices
Amount of dices that could be cut out from the blocks in Group
B
= 2 X ( 10 X 6 X 2 ) = 240 dices
Amount of dices that could be cut out from the blocks in Group
C
= 3 X ( 6 X 3 X 2 ) = 108 dices
Largest number of dices that could be made from the wooden
blocks
= Total amount of dices
= 90 + 240 + 108
= 438 dices
