A square based rectangular prism is to have surface area of 250cm^2 and volume Vcm^3.
I) show V =( 125x-x^3)/2

I get this part but I don’t get part II

II) find the dimensions for maximum volume.

I got the derivative and let it equal zero and got x = root 125/3. Then I got V’’ and found that it is less than zero and therefore a max but how do I get the dimensions. I know the length and width is just root 125/3 but what is the height

Let the dimensions be $l,\,w,\,h$.

$SA = 250 = 2lw + 2lh + 2 wh$

Since $l = w = x$,

$250 = 2x^2 + 4xh$

$\therefore h = \frac{250-2x^2}{4x}= \frac{125-x^2}{2x}$

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