- #1
rabbitstorm
- 6
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Homework Statement
A cylindrical can is to hold 500 cm^3 of apple juice the design must take into account that the height must be between 6 and 15 cm, inclusive. How should the can be constructed so that a minimum amount of material will be used in the construction? assume no waste.
Homework Equations
V is volume and SA is surface area
V= (pi)r^2h
SA=2(pi)rh + 2(pi)r^2
The Attempt at a Solution
so far this is what I have:
15>h>6
v=(pi)r^2h
500=(pi)r^2h
500/(pi)r^2=h
SA=2(pi)r(500/(pi)r^2) + 2(pi)r^2
Now I believe I need to find the derivative and set it to zero then solve for r.
The problem is that I can't quite figure out how I'm supposed to find the derivative if someone could give me a hand understanding the process I would really appreciate it as I have forgotten and my teacher is busy with the latest stuff.
Thanks,
~RS