A crate contains cylindrical cans of soup for shipment. Each crate is a cube with side lengths of 14in. Each soup can is 6in tal
l 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.
1 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.
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.
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