A box with a square base and no top must have a volume of 10 000 cm3. If the smallest dimension is 5 cm, determine the dimensions of the box that minimize the amount of material used.

Hey! We 've verified this expert answer for you, click below to unlock the details :)

I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!

By the way this is an optimization problem.

You need the formula for surface area here. That is S=x^2 + 4xy, so the formula for the volume of this box is (x^2)y=10,000 cm3. Solve for y and you get y=(10000/(x^2)). You can plug this into the original SA equation, so it has a single variable, then set the derivative equal to zero. Plug the number you get into the second derivative and if it is a negative number, than it is a max and if it is positive, then it is a min.

whoa

Looking for something else?

Not the answer you are looking for? Search for more explanations.

## More answers

Looking for something else?

Not the answer you are looking for? Search for more explanations.