# Calculus-Optimal Form: need help... please

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Suppose you are designing a coffee creamer container that has a volume of 48.42 cubic inches. Use the surface area and volume of a cylinder to develope an eqn. relating radius r and surface area S.
¡Ç=pi=3.14

S=2¡Çr^2+2¡Çrh
V=¡Çhr^2

• Calculus-Optimal Form: need help... please -

Yes
S = 2 pi r^2 + 2 pi r h
V = pi r^2 h
so
h = 48.42 / pi r^2
so
S = 2 pi r^2 + 2 pi r (48.42 /pi r^2)
S = 2 pi r^2 + 96.84/r

• Calculus-Optimal Form: need help... please -

Now I am sure you want to find what r is best for this volume (uses the least metal for area)
dS/dr = 4 pi r - 96.84/r^2
= 0 for max or min of S
4 pi r^3 = 96.84

• Calculus-Optimal Form: need help... please -

thnx! :)

how do i find the optimal radius?

• Calculus-Optimal Form: need help... please -

We did, read my second answer. I knew that would be next.
4 pi r^3 = 96.84

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