Calculate Length of Tinfoil Roll from Mass & Thickness

[JUSTaROCK]

Homework Statement

Aluminum, which has a mass of 2.7 grams for each cubic centimeter of volume, can be rolled into thin sheets
which your grandparents probably called "tinfoil." If a lump of aluminum of mass 0.75 kg is rolled into such a
sheet 18 μm thick and 25 cm wide, approximately how long is this roll of "tinfoil?"

Homework Equations

v = m/p p = density
v = L * A
surface area of circle = 4pi(r)^2
area of circle = pi(r)^2

The Attempt at a Solution

I have spent a lot of time on this problem but i can't seem to get it right i do not know what to do with the width or the thickness. I have tried to play it off like the width is the diameter,(which seems possible), but i just don't know what to do i have been working on this problem for 2 days now and i can't figure out what to do with it, please help i have a final on this tomorrow and i see it a lot in the old exams so i would like to know how to approach it if the problem gives thickness and width.

 

[zachzach]

Homework Statement

Aluminum, which has a mass of 2.7 grams for each cubic centimeter of volume, can be rolled into thin sheets
which your grandparents probably called "tinfoil." If a lump of aluminum of mass 0.75 kg is rolled into such a
sheet 18 μm thick and 25 cm wide, approximately how long is this roll of "tinfoil?"

Homework Equations

v = m/p p = density
v = L * A
surface area of circle = 4pi(r)^2
area of circle = pi(r)^2

The Attempt at a Solution

I have spent a lot of time on this problem but i can't seem to get it right i do not know what to do with the width or the thickness. I have tried to play it off like the width is the diameter,(which seems possible), but i just don't know what to do i have been working on this problem for 2 days now and i can't figure out what to do with it, please help i have a final on this tomorrow and i see it a lot in the old exams so i would like to know how to approach it if the problem gives thickness and width.

Think about the sheet of the foil before you roll it up. What shape is it?

 

[JUSTaROCK]

rectangle? so find the area of it as a rectangle ok ha ha don't know why i never thought of that

 

[zachzach]

rectangle? so find the area of it as a rectangle ok ha ha don't know why i never thought of that

A rectangle yes, but you are interested in the volume since the density is mass over volume.

 

[rdl]

As a scientist, it is important to approach problems with a systematic and logical method. In this case, we are given the mass of aluminum, its density, and the thickness and width of the rolled sheet. The first step is to calculate the volume of the aluminum sheet using the given density and mass. This can be done using the equation v = m/p, where v is the volume, m is the mass, and p is the density.

Once we have the volume, we can use the equation v = L * A to calculate the length of the sheet, where L is the length and A is the cross-sectional area. The cross-sectional area can be calculated by multiplying the width and thickness of the sheet.

However, we must take into account the fact that the sheet is rolled into a cylindrical shape. This means that the cross-sectional area is actually the surface area of a cylinder, which can be calculated using the equation 4πr^2, where r is the radius.

To find the radius, we can use the width of the sheet as the diameter, since it is mentioned that the width is approximately the same as the diameter of the sheet. Therefore, the radius would be half of the width.

Putting all of these equations together, we get v = L * 4π(r^2), where r = width/2.

Now, we can substitute the values given in the problem and solve for L. Once we have the length of the sheet, we can convert it from meters to centimeters to get the final answer.

In summary, the key steps in solving this problem are:
1. Calculate the volume of the aluminum sheet using the given mass and density.
2. Calculate the cross-sectional area of the sheet by multiplying its width and thickness.
3. Use the cross-sectional area to calculate the length of the sheet by considering it as a cylindrical shape.
4. Convert the length from meters to centimeters to get the final answer.

I hope this helps in your understanding and approach towards solving similar problems in the future. Remember to always break down a problem into smaller, manageable steps and use the relevant equations to solve for the unknown variables. Good luck on your final exam!