Determine the dimensions of a rectangular solid (with a square base) with maximum volume if its surface area is 337.5 square centimeters

Question

anonymous · Answer

First model your problem; draw the rectangle and write down some equations for the surface area and volume.

anonymous · Answer

matt can you please help me again? after this?

anonymous · Answer

Sure @cgoel

anonymous · Answer

I have v=x^2*y and x^2+4xy

anonymous · Answer

Well done.  I will tell you that the maximum volume of a rectangular box is maximized when x = y.

anonymous · Answer

and also, the surface area of the box should be
$$2x ^{2}+4xy = 337.5$$

anonymous · Answer

Am i supposed to take the first derivative of the 2x^2=4xy=337.5 after I get y to one side?

anonymous · Answer

No, you don't have to take the derivative.  If you want to take the derivative of something, you could divide Volume by Surface Area and set the derivative of that equal to zero to show that x = y in the optimal Volume vs. Surface Area box.

anonymous · Answer

Got it, thanks