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# Can problem

A cylindrical can is made from 6906cm^2 of aluminum and has a radius of 16 cm. find the height of the can.

### 1 Answer by Expert Tutors

Robert A. | Certified Teacher and Engineer - Tutoring Physics, Maths, and SciencesCertified Teacher and Engineer - Tutorin...
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The circumference = (Pi)d = 2 (Pi)r
The circumference is the width of the square piece of aluminum.
The height of the can is the height of the square.

So find the width then use that with area to find the height
from the formula W x H = Area

Width = C = 2(Pi)r = 2 x 3.14 x 16 cm = Width
You can do the math, right?

Then from Area = W x H find height

Area / W = H = 6906 cm2 / Width = Your Height
Can you do the math?

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I am editing my answer to see if this works.
When I try to add a comment Wyzant keeps deleting it !!!

Here is my 4th attempt. - Wyzant keeps deleting my additional comments.
Here is my third attempt at this - Wyzant keeps deleting my additional comments!!!!!
Wyzant just deleted all the answer to your comment - I'll try 1 more time.

You could look at it that way. I took it to mean just the sides of the cylinder.
To also cut the top and bottom you would need to know the dimensions of the stock in order to cut it in the optimum way. SO you do not have enough information.

For instance - it the stock was 6906 cm x 1 cm it would not be possible at all.
If the stock was 16 cm x 431.635 cm (the width of the radius) still not possible.
If the stock was 32 cm x 215.8125 cm (the width of the diameter) you could cut
|t|b|long piece| the top then bottom then have a long piece left over to find the tallest side piece from.
If the stock was 64 cm x 107.90625 cm (the width of top+bottom) you could cut
|t|short|
|b|piece| The top and bottom side by side the 64 cm edge then have a shorter but wider piece left over to find the tallest side piece from.

Of course maybe you were meant to also find the optimum dimensions of the stock piece, a much harder problem, and I don't know if this is for an algebra or calculus course.

What about the two circular bases ? Are the areas of these circles included in the 6906 cm^2 surface area ?
I never saw a cylindrical can without a top and a bottom. Just a thought.
I suppose you could look at that problem that way.
I took it to mean just the sides of the cylinder.
If you are going to find it with the top and bottom you do not have enough information.
You would need to know the shape and dimensions of the aluminum (AL) stock.
Only knowing that could you find the most efficient way to cut the stock to get the required pieces.
(unless you ignore the selvage (waste) around the circles, etc.)
For instance: for a piece of AL 6906 cm by 1 cm it would not be possible at all.
Cutting the pieces from other L's and W's of AL would possibly give different results.
- If cutting from a 32 cm x 215.6875 cm would give one result
A piece just wide enough to get a top would have the cut pattern
|t|b|long piece|
- If cutting from a 64 cm x 107.843375 might give a different result
|t|shorter|
|b|piece  |
So to optimize it you need to know the pattern to cut the pieces out of the stock.