# calculus

a. A closed cylindrical can is to hold 1000cm^3 of liquid. How should we choose the height and radius of this can to minimize the amount of material need to manufacture the can?

b.a manufacturer wants to design a open box having a square base and surface of 108cm^2. What dimensions will produce a box with minimum volume?

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3. 👁 830
1. πr^2 h = 1000, so h = 1000/(πr^2)
surface area is

a = 2πr^2 + 2πrh
= 2πr^2 + 2000/r

da/dr = 4πr - 2000/r^2
= 4(πr^3 - 500)/r^2
da/dr=0 when r = ∛(500/π)
thus, h = 100/∛(250π)

Do the other along the same way.

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posted by Steve
2. steve bro...
hw bout the b?
plz tell me...

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posted by dinesh
3. dinesh bro...

the b is the same as the a

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posted by Rick
4. h=234.43

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posted by dejen

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posted by dejen

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posted by abebe
7. -1+x^2

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posted by abebe

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