A can producer must make a cylindrical can that contains a volume of 16 ¶ cubic centimeters. Find the function this producer must analyze to make sure the amount of material is the least possible.
Originally Posted by bret80
The amount of matherial used is,
You want to minimize .
Note in first equation we have,
Thus,
Simplify (steps omitted),
Derivative time,
Make equal to zero,
Divide both sides by ,
Thus,
Note we substitute the value for "V":
Thus,
Square both sides,
Now take cube root,
\Originally Posted by bret80
This time, TPH, you've gone too far!!
(All he wanted was the equation to minimize. )
bret80: Follow the first two lines of TPH's thread, but instead of solving the Volume equation for r, solve it for h. Sub that value for h into the Area equation.
-Dan
Hello, Bret!
The correct answer I have is: 32/r + 2πr² . . . . not quite
The volume of a cylinder is: .
We are told that the volume is cm³.
So we have: . [1]
The surface area of a cylinder is: .top + bottom + side.
The top and bottom are circles of radius . .Their area is:
The side is a rectangle of length and height : area =
Hence, the surface area of a cylinder is: .
Substitute [1]: .
Therefore: .
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By the way, you can use &# 960; (without the space) to make π.
More codes (until you learn LaTeX):
&# 178; . . squared: ²
&# 179; . . cubed: ³
&# 8776; . approx: ≈
&# 8800; . not equal: ≠
&# 952; . . theta: θ
&# 177; . . plus/minus: ±
&# 176; . . degree: °
&# 8730; . radical: √
&# 183; . . dot: ·
&# 189; . . one-half: ½