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.

Printable View

- August 2nd 2006, 02:58 PMbret80Function of a cylinder
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.

- August 2nd 2006, 03:20 PMThePerfectHackerQuote:

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,

- August 2nd 2006, 03:49 PMbret80
The correct answer I have is

32/r + 2¶r^2 - August 2nd 2006, 04:03 PMtopsquarkQuote:

Originally Posted by**bret80**

This time, TPH, you've gone too far!!

(All he wanted was the equation to minimize. :D )

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 - August 2nd 2006, 09:20 PMCaptainBlackQuote:

Originally Posted by**ThePerfectHacker**

RonL - August 3rd 2006, 05:10 AMSoroban
Hello, Bret!

Quote:

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: .

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

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