how to find the dimensions of the rectangular box having the largest volume and surface area 150 square units?

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- Oct 29th 2008, 02:55 PMiwonderdimensions of box optimization
how to find the dimensions of the rectangular box having the largest volume and surface area 150 square units?

- Oct 29th 2008, 03:14 PMskeeter
completely closed box or an open top box?

- Oct 29th 2008, 04:11 PMiwonder
completely closed...thankyou

- Oct 29th 2008, 05:04 PMskeeter
I was afraid you'd say that.

The max volume for a closed box with a fixed surface area will be a cube.

Here is the work ...

let x , y , and z be the length, width, and height.

since

since ...

set both partials = 0 ...

combine both equations ...

since ...

the "cube" - Oct 29th 2008, 05:14 PMiwonder
thankyou very much, i really appreciate it!!!