Answer: 560
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Work Shown:
Let's find out how many smaller cubes are needed to go along the 2 & 2/3 inch side length of the bigger box.
First convert to an improper fraction
2 & 2/3 = 2 + 2/3 = 6/3 + 2/3 = 8/3
Divide this over the side length of the small cube to get
8/3 divided by 1/3 = (8/3)*(3/1) = 24/3 = 8
So we need exactly 8 small cubes along the 2 & 2/3 inch side length.
Let A = 8 so we can use this later.
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Repeat the same steps for the 3 & 1/3 inch side length
3 & 1/3 = 3 + 1/3 = 9/3 + 1/3 = 10/3
10/3 divided by 1/3 = (10/3)*(3/1) = 30/3 = 10
We need 10 cubes along the 3 & 1/3 inch side length.
Let B = 10.
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Repeat for the 2 & 1/3 inch side length
2 & 1/3 = 2 + 1/3 = 6 + 1/3 = 7/3
7/3 divided by 1/3 = (7/3)*(3/1) = 21/3 = 7
We need 7 cubes along the 2 & 1/3 inch side length
Let C = 7
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Multiply out the values of A,B,C to get
A*B*C = 8*10*7 = 560
This means we need 560 cubes that are each 1/3 of an inch along the the side to fill up a box that has dimensions of 2 & 2/3 inches by 3 & 1/3 inches by 2 & 1/3 inches.