A community for students.
Here's the question you clicked on:
 0 viewing
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.
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.

This Question is Closed

LordHades
 3 years ago
Best ResponseYou've already chosen the best response.2By the way this is an optimization problem.

brainshot3
 3 years ago
Best ResponseYou've already chosen the best response.1You 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.

aminah.love18
 3 years ago
Best ResponseYou've already chosen the best response.0@lord id listen to the Brain

LordHades
 3 years ago
Best ResponseYou've already chosen the best response.2I did that. I got an answer. It seems to be wrong. And, that way we don't use the information: "Smallest dimension is 5"

brainshot3
 3 years ago
Best ResponseYou've already chosen the best response.1I 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.

brainshot3
 3 years ago
Best ResponseYou've already chosen the best response.1The first derivative I had was: \[2x  40000/x^{2} =0\] The second derivative was: \[2 + 40000/x^{3}=0\]

LordHades
 3 years ago
Best ResponseYou've already chosen the best response.2Thank you. That seems to be right.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.