So I know the volume of a golf ball is est. 2.482 given if the ball is 1.68″ in diameter and plug that into the formula to get the volume of a sphere. (4/3*pi*r^3). And 5 gallons converted to cubic inches is 1155 cubic inches. So I would reckon to find this we would divide 1155 by 2.482 = 465 (if being unable to put in a fraction of a ball)….this seems like a lot. but I know we cannot pack sphere’s to occupy the entire volume, there will be spacial loss….so my guess is between 232325….anybody got a closer answer? Tried to ask this in the golf section but they just told me to fill a bucket up with golf balls and count them…..lol.
3 Answers

Try this instead….
consider a cylinder insead of a sphere…(not sure why you chose that…)
the diameter of a 5 gal bucket is about 11 inches on average.
so imagine if we layered the balls on the bottom layer as tightly as possible…with a “top down view”, we can estimate how many 1.68 circles fint into a 11.0 circle…again, you have spacial loss like you mentioned, but ignore it for now…
the area of that bucket bottom is (pi)(5.5)^2 = about 95 sq inches
using your size for the ball, i estimated the approximate size of a box of balls (12) and found that to be about 34sq inches…so we could fit roughly 2.8 boxes of balls on the bottom layer (about 35 balls)
now, lets assume for measurements sake that we can stack all of the balls exactly on top of each other to form layer after layer….this assumption gives us a known fact of the number of balls that will surely fit in the bucket….
a 5 gallon bucket is about 15 inches deep, divide that by the ball size….we get about 9 layers from top to bottom….that tells us that we know for sure we could fit 315 balls (35 per layer, 9 layers) in the bucket…which is way more than your guess….and the reason why, is you cut off way too much of your initial work due to the spacial loss….
Now obviously, we cant stack the balls perfectly on top of each other, layer by layer…to account for spacial loss, if you are able to drop a few balls in a bucket, you will notice that the loss really isnt too bad, this is due to the wonderful properties of spheres that allow them to settle and rest against each other better than other 3D figures. When you start pouring balls in they really pack together nicely….just look at a bag of refurbished balls at kmart or walmart….not much gap between them….
One last thing to note….if we were able to stack the balls perfectly, it would not take long to see there are some huge gaps after some observations it looks like for each gap between 2 layers, the total volume could fit an extra 45 balls when said and done….that being said….with 9 layers (including rounding off the top of the bucket) that adds the potential for about 3645 more balls….
giving us a grand total of about 350360 balls when the balls would collapse upon each other. This seems valid enough to me…when I hit a “large” bucket of balls at the range, they tell me there are about 325350 balls in it….its the approximate size of a 5 gallon bucket, just shorter and a lager base…
Hope this is enough evidence for you to sway your opinon a bit….I have to admit it was rather fun investigating….

Bucket Of Golf Balls

This is difficult to understand for me too