xyz block
A grid has just enough material removed such that the front side projects an the right side a and the top side a The orthogonal views of these letters are shown below.
An isometric view of the final shape is shown below.
What is the volume of this figure?
The answer is 21.333333333.
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1 solution
Here are each of the four layers separated and then color-coded by volume. (They are viewed from above the X so you can see the remains of the Z's from each layer, but they are turned sideways.)
Red: whole unit cubes: 10 of them.
Orange: half cubes: 16 of them.
Yellow: one-third cubes: 4 of them.
Green: one-sixth cubes: 12 of them.
Total volume 1 0 + 2 1 6 + 3 4 + 6 1 2 = 3 6 4 ≈ 2 1 . 3 3 3 3 3 3
Interestingly, exactly one-third of the original cube remains.