SOLUTION: The interior dimensions of a carton in the shape of a rectangular prism are 2 ft by 1ft by 1 1/2 feet. How many boxes, each in the shape of a cube with 1-inch edges, will fit i

Question 253845: The interior dimensions of a carton in the shape of a rectangular prism are
2 ft by 1ft by 1 1/2 feet.
How many boxes, each in the shape of a cube with 1-inch edges, will fit inside
the carton?
I think the answer is 36 cubes, but I want to make sure.
the volume = lxwxh, so the volume would be 3 cubic feet. Then I thought that
there would be 36 inches in 3 feet so maybe the answer was 36 cubes.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
2 feet by 1 foot by 1.5 feet = 24 inches by 12 inches by 18 inches.
volume of the carton is 24*12*18 = 5184 cubic inches.

each smaller box is 1 cubic inch (1*1*1).

24 cubes can fit along the 24 inch side.
18 cubes can fit along the 18 inch side.
assuming the height is 12 inches, then 12 cubes high.

on the bottom of the box, we have 18 rows of 24 cubes each.
that's 18*24 = 432 cubes on the first inch of height.
there are 11 more inches of height which makes 11 * 432 = 4752 cubes.
4752 + 432 = 5184 cubes in total.

the dimensions of the large carton were in feet.

you needed to convert them to inches.

there are 12*12*12 cubic inches in a cubic foot.

that equals 1728 cubic inches per cubic foot.

3 * 1728 = 5184 cubic inches which is the same as I calculated earlier.

each smaller box is 1x1x1 = 1 cubic inches indicating that 5184 of the smaller boxes should fit into the larger carton unless there's some dead space where a smaller cube won't fit. There was none, so 5184 smaller boxes fit into the larger carton.

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