Finding the number of spheres in a graduated cylinder

[brotivation]

Homework Statement

This is from a worksheet. I had to find the volume myself

"A large number of spheres are poured into a graduated cylinder and gently vibrated until the occupy a minimum volume of 40 mL (or 40 cm^3). Use the information about close packing and the data you found to find the number of spheres in the cylinder. "

I found -- volume = 0.0477 cm^3
diameter = 4.5 mm
Given -- close packing fraction = .74048

Homework Equations

Wasn't given one but I used (minimum volume) / (volume of a sphere)

The Attempt at a Solution

40 cm^3 / 0.0477 cm^3 = 839 spheres



I'm not sure if I did was right. I don't know what I'm supposed to do with the information about the close packing fraction. I can't find it in my book.

 

[SammyS]

Homework Statement

This is from a worksheet. I had to find the volume myself

"A large number of spheres are poured into a graduated cylinder and gently vibrated until the occupy a minimum volume of 40 mL (or 40 cm^3). Use the information about close packing and the data you found to find the number of spheres in the cylinder. "

I found -- volume = 0.0477 cm^3
diameter = 4.5 mm
Given -- close packing fraction = .74048

Homework Equations

Wasn't given one but I used (minimum volume) / (volume of a sphere)

The Attempt at a Solution

40 cm^3 / 0.0477 cm^3 = 839 spheres

I'm not sure if I did was right. I don't know what I'm supposed to do with the information about the close packing fraction. I can't find it in my book.

What does the close packing fraction tell you?

 

[brotivation]

It tells me that 26% of the used volume is wasted space.

 

[SammyS]

It tells me that 26% of the used volume is wasted space.

So, isn't 26% of the 40 cm³ volume, wasted space?

 

[brotivation]

So, isn't 26% of the 40 cm³ volume, wasted space?

Okay, so this is what I did.

40 cm^3 * .74048 = 29.6 cm^3

29.6 cm^3 / .0477 cm^3 = 621 spheres

Is this right?

10.4 cm^3 of the 40 cm^3 is wasted space leaving 29.6 cm^3 being used. So I would take the used value and divided by the volume of the sphere right?

 

[SammyS]

Okay, so this is what I did.

40 cm^3 * .74048 = 29.6 cm^3

29.6 cm^3 / .0477 cm^3 = 621 spheres

Is this right?

10.4 cm^3 of the 40 cm^3 is wasted space leaving 29.6 cm^3 being used. So I would take the used value and divided by the volume of the sphere right?

That seems reasonable !

 

[brotivation]

That seems reasonable !

Thanks a lot. It hit me right when I saw you said 26% lol.