# calculus

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)

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1. 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.

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bobpursley
2. Thank you very much

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3. What do you mean by with respect to zero?

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4. He said set the derivative to zero to solve for the maximum.
Max or min when dV/ds = 0

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5. Okay Thank You again

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6. Excuse me the volume equation for this problem is V=s^2 h?

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7. 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.

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8. 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?

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9. 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.

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bobpursley
10. ooo okay Thank You

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