How many 2 inch cubes can be placed completely placed inside a box that is 8 inches long, 2 inches wide, and 6 inches tall?Please show all work.

1 Answer

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justaguide | College Teacher | (Level 2) Distinguished Educator

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We see that the dimensions of the box are 8 inches * 2 inches * 6 inches. All the three sides are multiples of 2. So it is possible to fill the entire volume of the box with 2-inch cubes without leaving any space unoccupied.

To determine the number of cubes that can be placed we need to find the volume of the box which is

8*2*6 = 96 inch^3

The volume of one cube is 2*2*2 = 8 inch^3

The number of cubes that can be placed is 96/8 = 12.