How many golf balls fill the can

[Kenzie]

A cylindrical can contains an unknown number of golf balls. The can has a height of 10 inches and a volume of 15.625 Pi inches cubed. How may golf balls fill the can if they are uniform in size to the container?

 

[Steven G]

A cylindrical can contains an unknown number of golf balls. The can has a height of 10 inches and a volume of 15.625 Pi inches cubed. How may golf balls fill the can if they are uniform in size to the container?

What is the size of a golf ball?

 

[Kenzie]

The word problem did not give this information but I looked up on Google and the standard US golf ball has a diameter of 1.68 inches.

 

[Steven G]

The word problem did not give this information but I looked up on Google and the standard US golf ball has a diameter of 1.68 inches.

I know that I am exaggerating but if the golf ball is the size of a basketball then no golf balls could be put into the can. On the other hand if the golf ball is the size of a small ball bearing then there would be many golf balls in the can. So your answer will be in the middle. I have the gut feeling that the answer will depend on how you arrange the balls in the can--it will make a small difference but none the less a difference. I will see if everything works work perfectly and will reply back.

 

[Steven G]

I know that I am exaggerating but if the golf ball is the size of a basketball then no golf balls could be put into the can. On the other hand if the golf ball is the size of a small ball bearing then there would be many golf balls in the can. So your answer will be in the middle. I have the gut feeling that the answer will depend on how you arrange the balls in the can--it will make a small difference but none the less a difference. I will see if everything works work perfectly and will reply back.

I prefer to assume that the radius of the golf ball is .75 inches. So how many golf balls can you put in one layer. Hint, how many golf balls can you but around a centered golf ball? How many layers can you put?

 

[Kenzie]

I have no idea. This is the exact verbiage from the homework assignment the teacher gave. I am just going to get help tomorrow morning. Thanks for trying to help.

 

[Ishuda]

"uniform in size to the container": whadda heck does that mean?

Since the container is cylindrical, I would think that the diameter of the container was the same as the diameter of the spherical golf ball.

If so, let r be the radius [= d/2] in inches of the golf ball, then the volume of the container is \(\displaystyle \pi r^2 h\) and the number of golf balls which would fit in the container is [ h/(2r) ] where [] indicates the floor function. So
\(\displaystyle \pi r^2 h = 15.625 \pi\)
or
h = 15.625 / r²
or the number of golf balls N which fit inside the container is given by
N = [7.8125 / r³]

 

[Steven G]

Since the container is cylindrical, I would think that the diameter of the container was the same as the diameter of the spherical golf ball.

If so, let r be the radius [= d/2] in inches of the golf ball, then the volume of the container is \(\displaystyle \pi r^2 h\) and the number of golf balls which would fit in the container is [ h/(2r) ] where [] indicates the floor function. So
\(\displaystyle \pi r^2 h = 15.625 \pi\)
or
h = 15.625 / r²
or the number of golf balls N which fit inside the container is given by
N = [7.8125 / r³]

What do you think about what I said about the radius of the golf balls be .75 inches? You need to draw out what I am thinking. Think 2-d and ask yourself how many quarters can you place around a single quarter. The answer is 6 (verify it as it is fun!) So one layer will have 7 golf balls that use a height of 1.5 inches. ....

 

[Steven G]

I have no idea. This is the exact verbiage from the homework assignment the teacher gave. I am just going to get help tomorrow morning. Thanks for trying to help.

You really will not get any help tomorrow as the working in this problem is flawed. I showed you how you can get 0 golf balls in the can all the way to a very very large number of balls. A google search showed that the diameter of golf balls actually vary in size. So how can you expect this problem to be done?

 

[Ishuda]

What do you think about what I said about the radius of the golf balls be .75 inches? You need to draw out what I am thinking. Think 2-d and ask yourself how many quarters can you place around a single quarter. The answer is 6 (verify it as it is fun!) So one layer will have 7 golf balls that use a height of 1.5 inches. ....

Were the container big enough to contain several balls on one layer then you would have to start worrying about the layout of the several balls. Right now, I prefer not to think about that.

 

[Steven G]

Another problem-setting-teacher that should be fired

I am afraid to say any comment here but you know how I feel about this (just think about how my hand would look if I was hitchhiking)!