Asked by Barbara

Find the dimensions of the largest open-top storage bin with a square base and vertical sides that can be made from 108ft^2 of sheet steel. (Neglect the thickness of the steel and assume that there is no waste)
Answered by bobpursley
The volume is s^2 h
the surface area is s^2+ 4sh but

108=s^2+4sh
h=108/4s -s/4

put that into the volume equation for h, then take the derivative of V with respect to s, set to zero, and solve for s.
Answered by Barbara
Thank you very much
Answered by Barbara
What do you mean by with respect to zero?
Answered by Damon
He said set the derivative to zero to solve for the maximum.
Max or min when dV/ds = 0
Answered by Barbara
Okay Thank You again
Answered by Barbara
Excuse me the volume equation for this problem is V=s^2 h?
Answered by Damon
Yes, s^2, the side times the side, is the area of the base.
That times the height h is the volume of the box that you wish to maximize.
Answered by Barbara
Okay but now I'm confused because when I find the derivative of the volume I get dv/dt=2s(ds/dt) then I don't know the rest because I have to find the derivative for 108/4s -s/4 which equals to h but what would be its derivative?
Answered by bobpursley
V=s^2 h= s^2 (108/s - s/4)
= 108s-s^3/4
dv/ds=0=108-3/4 s^2
now solve for s.
Once you get s, you can solve for h.
Answered by Barbara
ooo okay Thank You
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