minimization: a cube has a square base of width x....

[ssabadnama3]

a cube has a square base of width x and has a height of y. find the dimensions of x and y for which the volume is 12 and the surface area is as small as possible. ok V=side^3, does x=y and what do i do with the surface area?

 

[mmm4444bot]

Are you sure the object is a cube?

You're right about the volume; it's x^3 because x = y, for a cube.

There is only one value for the surface area of any given cube, so it does not make sense (to me) to ask about minimizing this value.

Please double-check the given information.

 

[ssabadnama3]

that is the exact question. if it helps any the one below it is similar and i couldn't answer it either.
Find the dimensions x and y for which the surface area is 20 and the volume is as large as possible. and it is talking about a cube also. thanks for answering sorry if its a confusing qusetion. i appreciate the help

 

[galactus]

Find the dimensions x and y for which the surface area is 20 and the volume is as large as possible. and it is talking about a cube also. thanks for answering sorry if its a confusing question. i appreciate the help

Technically, it is not a cube because \(\displaystyle x\neq y\). It is a rectangular paralellepiped. In other words....a box.

The surface area is \(\displaystyle 2x^{2}+4xy=20\)

The volume is \(\displaystyle V=x^{2}y\)

Solve the surface area for y and sub into the volume equation. It will be in terms of x alone. Differentiate, set to 0 and solve for x.