Thread: Numbers of balls in a frustum

1. Numbers of balls in a frustum

I am unable to solve this question, helps needed !!

I need to calculate how many balls can be put into the frustum.

Basically i m using frustum of a cone formula to calculate the whole volume.

Frustum Volume = (p * height * (RaČ + Ra * Rb + RbČ) / 3)
= (p * 72 * (81+135+225) / 3 )
= 33250.61665

However for the oval shape item, i do not know how to calculate it. Any idea what formula i should use?

My idea is using the (total frustum volume - oval shape volume) / 1.5 to get the numbers of balls that can be place in the glass. Is my assumption right? I was told the number of balls can be place in is within the range of 3000 to 8000. Please advice.

2. Originally Posted by williamlcs
I am unable to solve this question, helps needed !!

I need to calculate how many balls can be put into the frustum.

Basically i m using frustum of a cone formula to calculate the whole volume.

Frustum Volume = (p * height * (RaČ + Ra * Rb + RbČ) / 3)
= (p * 72 * (81+135+225) / 3 )
= 33250.61665

However for the oval shape item, i do not know how to calculate it. Any idea what formula i should use?

My idea is using the (total frustum volume - oval shape volume) / 1.5 to get the numbers of balls that can be place in the glass. Is my assumption right? I was told the number of balls can be place in is within the range of 3000 to 8000. Please advice.
This is a sphere-packing problem. A Google search turns up several useful links (second and third) which you should read to get an idea for what's involved in the problem. Your assumption for the formula is not correct.

3. Originally Posted by williamlcs
I am unable to solve this question, helps needed !!

I need to calculate how many balls can be put into the frustum.

Basically i m using frustum of a cone formula to calculate the whole volume.

Frustum Volume = (p * height * (Ra&#178; + Ra * Rb + Rb&#178 / 3)
= (p * 72 * (81+135+225) / 3 )
= 33250.61665

However for the oval shape item, i do not know how to calculate it. Any idea what formula i should use?

My idea is using the (total frustum volume - oval shape volume) / 1.5 to get the numbers of balls that can be place in the glass. Is my assumption right? I was told the number of balls can be place in is within the range of 3000 to 8000. Please advice.
It seems to me that you don't have (or haven't given us) sufficient
information to calculate the volume of the glass.

Are the dimples parts of the surface of spheres? How many are there?
How far are their centres from the axis of the glass? how far below the
rim are the centres of the spheres?

Even with this information I would not want to calculate the volume
of this glass!

(Having said that it seems that 3-D hit-or-miss Monte-Carlo integration
might not be too bad for this - actually it would be quite neat)

After having calculated the volume you will still need to use the packing
fraction you will find from following JakeD's link to find the number of
balls.

RonL