Calculating dimensions from area and volume

[fran1942]

Hello, my question is:

A rectangular piece of sheet metal with area of 1200cm^2 is to be bent into a cylindrical pipe having a volume of 300cm^3. What are the dimensions of the sheet of metal ?

Can someone please give me a pointer as to how to go about solving this. I struggle with math.

Thanks kindly for any help.

 

[danago]

Try drawing a rectangle with width W and length L. Now try to visualize how W and L relate the radius and height of the cylinder that it becomes. Use these relationships to write equations for the radius and height in terms of L and W, and then come up with an equation for the volume. See if you can find the dimensions from there.

If it helps you to visualize it, maybe try taking a rectangular piece of paper and rolling it into a cylinder.

 

[fran1942]

thanks.

my volume here will be:
300cm^2 = pi * r^2 * h

my area will be:
1200cm^2 = 2 pi r * h

however I can't see how to solve this without a radius or height dimension.

Can anyone please help ?

 

[Dick]

thanks.

my volume here will be:
300cm^2 = pi * r^2 * h

my area will be:
1200cm^2 = 2 pi r * h

however I can't see how to solve this without a radius or height dimension.

Can anyone please help ?

You mean 300cm^3 for the volume. Divide the first equation by the second equation.

 

[Mark44]

Or as an alternative, solve for h in one equation, and substitute that value in the other equation.

 

[fran1942]

sorry guys, I still can't grasp it - arggghhh.
Could someone please type out the process mentioned above with the solution. Once I see what you are doing I will get it.
(I am trying to find the dimensions of the sheet.)

Thanks kindly.

 

[Mark44]

Omitting the units, your equations are
300 = π r²h and
1200 = 2 πrh

Dividing the first equation by the second (Dick's suggestion) gives
1/4 = r/2, or r = 1/2 (cm). Note that what you're doing is dividing each side of the first equation by equal quantities, 1200 and 2 πrh, to produce a new equation. In the division the π and h factors cancelled.

The rectangular piece of sheet metal is very much longer than it is wide.

 

[fran1942]

thanks, I follow that.
So I can now calculate the dimensions with the r value of .5
That gives me a set of dimensions for the sheet measuring 381.97 x 3.14cm

Hopefully I have got this right ?

Thanks kindly for your persistence.

 

[Mark44]

It's better to leave them in their exact values, rather than the approximations you got. The dimensions are 1200/π and π. Your dimensions give a volume of about 1199.4 cm^3.

 

[Dick]

thanks, I follow that.
So I can now calculate the dimensions with the r value of .5
That gives me a set of dimensions for the sheet measuring 381.97 x 3.14cm

Hopefully I have got this right ?

Thanks kindly for your persistence.

Try it out. Does that give you an area of 1200cm^2 and a volume of 300cm^3?