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

- Calculus-Optimal 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

- Calculus-Optimal 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

- Calculus-Optimal 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?

- Calculus-Optimal 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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