PROBLEM: Volume of a Can
What is the volume of a 12 ounce can?
This was easy to start out with the volume of a circular cylinder.
In other words, how may cubic inches in a 12 oz can? Make a guess. Measure the radius and height of a soda can and compute an estimate.
Alright taking a guess, I first came up with the the measurements of the can itself, although just from looking at the can, anyone can see that its shape is not regular...in fact, it has a partial sphere shape at the end or bottom of the can (as if someone purposefully put a ball at the bottom to make my life harder). The top is also a bit rounded and the soda does not even reach the very top of the can. So it is debatable as to whether I am actually measuring the volume of what the can CAN hold and what the can ACTUALLY holds.
I started with the measurement of a can of my Canada Dry. (I love ginger ale!)
The diameter (and radius), height, and the circumference are given below:
Now if I plug my numbers into my equation from above, I get:
But still, remember we said that the Canada Dry can's contents contain the ginger ale that does not fill to the top of the can and the can itself is not a true cylinder, therefore, we must find the actual measures of the top and bottom of the can as well as the actual radius by measuring off the circumference with a piece of string and measuring it against a ruler or in my case, a yard stick.
Once I measured the can's circumference, I got about 8.7 inches, so my radius would be
Now when we plug r into the volume equation, we get:
The top and bottom of the can seem harder to deal with, but I just measured the bottom of the can with a string again and I got right at .38 inch, and then I measured the top of the can and got about .125 inch. Shae was saying that since the can was shaped the way it was, we had to take the "whole" can into consideration. We, therefore, had to consider taking an inch or two off the height due to this wonderful way the can was created and we had to keep in mind that the can's top and bottom also had very small circular cylinders within them. So, here, take a inch or two off the height.
I would probably estimate that if we were to take an inch off the height, then the volume of the 12 ounce can would be:
I would probably estimate that if we were to take two inches off the height, then the volume of the 12 ounce can would be:
Now we take all our data and just average them out to get a close approximation of the volume of a 12 ounce can:
How many cubic centimeters are in a 12 ounce can?