A crate contains cylindrical cans of soup for shipment. Each crate is a cube with side lengths of 14in. Each soup can is 6in tall and has a diameter of 3.5in How many soup can will fit in each crate? Use 3.14 for π. Explain how you got your answer.

Each cube has a side length of 14 in.

Each can of soup is 6 in tall and has a diameter of 3.5 in.

Refer to the figure shown below.

Top view:

For each side of the crate, number of cylinders that can fit in the crate is

14/3.5 = 4

Therefore 4² = 16 cylinders can be fitted in the crate (top view).

Side view:

The number of cylinders that can be stacked up in the crate is

14/6 = 2.333

Therefore only 2 rows are cylinders can be stacked up.

The total number of cylinders that will fit in a crate is 16*2 = 32.

Note:

Computing volumes for the crate and for a soup can will give wrong answers.

The volume of a soup can is V₁ = (3.14/4) * (3.5²) * 6 = 57.6975 in³

The volume of a crate is V₂ = 14³ = 2744 in³

Therefore

V₂/V₁ = 47.55, that is 47 cans per crate.

The problem is that the geometry of the cans will make it impossible to fit 47 cans into the cube.

Answer: 32 soup can per crate.