Question

A cereal box is designed to hold a volume of 4096 cubic centimetres of cereal.

What dimensions will minimize the cost of producing the box?

Answer 1

Refer to the step-by-step

Explanation:

To minimize the cost of producing the box, we would want the box to be a cube.

Where the volume,
`V=s^(3)`, where s is the length of one side of the box.

We were given the value,
`V=4096 cm^(3)`, plug this into the equation above so we can find the dimensions of the box...

`4096=s^(3) = > s=\sqrt[3]{4096} = > s=16`

Thus the dimensions to minimize the cost of the production of the box would be 16cm by 16cm by 16cm.