SOLUTION: A box with a square base and closed top is to hold 1000 cm3. Find the dimensions that require the least material (assume uniform thickness of material) to construct the box.

Algebra ->  Volume -> SOLUTION: A box with a square base and closed top is to hold 1000 cm3. Find the dimensions that require the least material (assume uniform thickness of material) to construct the box.      Log On


   

Question 1043885: A box with a square base and closed top is to hold 1000 cm3. Find the dimensions that require the least
material (assume uniform thickness of material) to construct the box.
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Let represent the measure of one side of the square base and let represent the measure of the height of the box.

Given that the volume of the box is , we know that the measure of a side of the base and the height have the relationship:



Two sides of the box have an area that measures and four sides of the box have an area that measures

So we write a function for the total surface area of the box as a function of the measure of one side of the base thusly:



Take the first derivative and set it equal to zero:





Solve for , then calculate

John

My calculator said it, I believe it, that settles it