You have been asked to design a rectangular box with a square base and an open top. The volume of the box must be 2916cm3. Determine the dimensions of the bin that will minimize the surface area, where x is the length of each side of the base and y is the height of the box. Enter an exact answer.

  x = 18 cm

  y = 9 cm

Step-by-step explanation:

An open-top box will have minimum surface area when it is in the shape of half a cube. The whole cube would have volume 2×2916 = 5832 cm³, so its side length would be ∛5832 cm = 18 cm.

The dimensions of the box are x = 18 cm; y = 9 cm.

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The surface area is x^2 +4xy, where y = 2916/x^2. That is, the surface area is ...

  S = x^2 +11664/x

Setting the derivative to zero, we find ...

  dS/dx = 0 = 2x -11664/x^2

  x^3 = 5832 . . . . . . . . may look familiar

  x = ∛5832 = 18

  y = 2916/18^2 = 9

this is a very good question

step-by-step explanation:

i got a hair cut today from my mom not to flex just to flex kim jon un is one rad fellow i'd say you'd need to take the hairline in kinda like a box shape like someone rammed a lego brick into your head. from there you really need to take the top up keeping with that boxy aesthetic, finally coat the whole thing with gel if your country economics are failing or whatever you can just coat it with the starving children's food rations. about 5 orphans per strand is a good ratio. good luck with the fresh cut my dude

step-by-step explanation:

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