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Part 1
A box is in the shape of a cube. The box has edge lengths of 9 in. How many unit cubes are needed to fill the box?
To find the number of unit cubes needed to fill the box, we need to calculate the volume of the box first.
Since the box is in the shape of a cube, all three edges have the same length of 9 inches.
The volume of a cube is given by the formula V = s^3, where s is the length of one side.
Therefore, the volume of the box is V = 9^3 = 729 cubic inches.
Since each unit cube has a volume of 1 cubic inch, the number of unit cubes needed to fill the box is 729.