Posted by Stephanie on Tuesday, November 4, 2008 at 7:46pm.
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

CalculusOptimal Form: need help... please  Damon, Tuesday, November 4, 2008 at 8:04pm
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

CalculusOptimal Form: need help... please  Damon, Tuesday, November 4, 2008 at 8:07pm
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

CalculusOptimal Form: need help... please  Stephanie, Tuesday, November 4, 2008 at 8:46pm
thnx! :)

optimal radius  Stephanie, Tuesday, November 4, 2008 at 9:07pm
how do i find the optimal radius?

CalculusOptimal Form: need help... please  Damon, Tuesday, November 4, 2008 at 9:58pm
We did, read my second answer. I knew that would be next.
4 pi r^3 = 96.84
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