Asked by Stephanie
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
¡Ç=pi=3.14
S=2¡Çr^2+2¡Çrh
V=¡Çhr^2
Answers
Answered by
Damon
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
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
Answered by
Damon
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
dS/dr = 4 pi r - 96.84/r^2
= 0 for max or min of S
4 pi r^3 = 96.84
Answered by
Stephanie
thnx! :)
Answered by
Stephanie
how do i find the optimal radius?
Answered by
Damon
We did, read my second answer. I knew that would be next.
4 pi r^3 = 96.84
4 pi r^3 = 96.84
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