Thread: "Find the volume of the largest open box.."

Here's the problem:

"Find the volume of the largest open box that can be made from a piece of cardboard 24 inches square by cutting equal squares from the corners and turning up the sides."

I have no provided diagram, the answer is 1024 cubic inches.

Here's what I've done:

V=x*y*z

y = z, y*z = 24.

y=z=square root of 24 - 2x, substitute into the equation for volume, differentiate, set v'(x) = 0, solve, figure out which one doesn't break my domain, substitute into the original equation...and it doesn't work.

Originally Posted by Wolvenmoon

Here's the problem:

"Find the volume of the largest open box that can be made from a piece of cardboard 24 inches square by cutting equal squares from the corners and turning up the sides."

I have no provided diagram, the answer is 1024 cubic inches.

Here's what I've done:

V=x*y*z

y = z, y*z = 24.

y=z=square root of 24 - 2x, substitute into the equation for volume, differentiate, set v'(x) = 0, solve, figure out which one doesn't break my domain, substitute into the original equation...and it doesn't work.

let = side length of squares cut from each corner











find and maximize

Originally Posted by Wolvenmoon

Here's the problem:

"Find the volume of the largest open box that can be made from a piece of cardboard 24 inches square by cutting equal squares from the corners and turning up the sides."

I have no provided diagram, the answer is 1024 cubic inches.

Here's what I've done:

V=x*y*z

y = z, y*z = 24.

y=z=square root of 24 - 2x, substitute into the equation for volume, differentiate, set v'(x) = 0, solve, figure out which one doesn't break my domain, substitute into the original equation...and it doesn't work.

Hi Wolvenmoon,

as the same size square is being cut from all 4 corners,
simply label the side of that removed square "x".

Then, since 2 squares are being removed from any side,
the base of the box is a square of sides 24-2x.
The height of the box is x.

The box volume of the bos is (base area)(height)=x(24-2x)(24-2x).

You can either multiply this out and differentiate wrt x
or use the product rule.