## LordHades 3 years ago 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.

By the way this is an optimization problem.

2. brainshot3

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.

3. aminah.love18

whoa

4. aminah.love18

@lord id listen to the Brain

5. brainshot3

Thank you =)

I did that. I got an answer. It seems to be wrong. And, that way we don't use the information: "Smallest dimension is 5"

7. brainshot3

I worked out the problem and I got 27.1442 as the minimum. I plugged it into the second derivative and got a positive answer, so it must be a min. as oppose to a max. You may have taken the wrong derivative.

8. brainshot3

The first derivative I had was: \[2x - 40000/x^{2} =0\] The second derivative was: \[2 + 40000/x^{3}=0\]