A crate contains cylindrical cans of soup for shipment. Each crate is a cube with side lengths of 12in. Each soup can is 5in tall and has a diameter of 4in How many soup can will fit in each crate? Use 3.14 for π. Explain how you got your answer.

The volume of the cube is base times width times height, or any of these measurements cubed, since they're all the same.

Therefore, the volume of the cube is:

12³ = 1728 in³

The volume of the cylinder is π*r²*h, where r is the radius and h is height

Remember that the diameter is twice the radius, so the radius is 2 in and the height is 5 in.

Therefore, each can has a volume of π * 2² * 5 = 20π

Approximating π as 3.14 ...

The volume of each can is 62.8 in³

1728 : 62.8 = 27.5

Rounding down, 27 cans can fit in the crate.

This is how I suspect the teach wanted you to solve, since it involves finding the volume of both shapes and using pi. However, this is not actually how many cans can fit, because it does not take into account the fact that not every inch of available space will be used.

Here is another way to solve, taking this fact into account, that gives the more accurate answer:

Each can has a diameter of 4in, which means that they each require a square of 4 x 4 in to accommodate their base.

The base of each can requires 16 in² of space in the crate.

The base of the cube is 12 x 12, so the area of the base is 144 in²

144 : 16 = 9, so the base of the cube, or bottom of the box, can fit 9 cans, arranged 3 by 3.

The cube has a height of 12 inches, and each can is 5 inches tall. Therefore, two of these stacks can fit in the box, for 9 x 2 = 18 cans.

This is a much better answer, as it takes into account the fact that the cans can't occupy every inch of available space in the cube.