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Question 83799: If you could fill a basketball with root beer, how many cans would it hold?
(12oz can & regulation NBA ball.)
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Hmmmm. I wonder if you are doing this as a math exercise or as an actual project. As a
math exercise you can make certain assumptions that you may not want to make if you are
performing a "real world" measurement.
.
Let's do it as a math exercise first. The circumference of an NBA basketball is (measured
in the grooves on the ball) 29.5 inches. Use the formula for circumference to find the radius
of an NBA basketball:
.
.
Substitute 29.5 inches for the circumference of the ball and you get:
.
.
Solve for R by dividing both sides by  to get:
.
.
Using a calculator to do the math on the left side results in:
.
 inches
.
Now you can find the volume of the basketball by using the formula for the volume of
a sphere:
.
.
Substitute 4.695070821 inches for R and the equation becomes:
.
.
Calculator time ... Using a calculator to perform the math on the right side of this equation
you should find that:
.
 cubic inches
.
Now assume that 12 oz of root beer is the same volume as 12 oz of water. At 39.164 degrees
Fahrenheit water weighs 0.036313 lbs per cubic inch and since a lb is 16 oz, we can multiply
this figure by 16 to find out that the density of water is:
.
 ounces per cubic inch. Therefore a 12 oz can contains
a volume of  cubic inches.
.
[Just as a sanity check, the approximate dimensions of a 12 oz can are about 1.25 inches
in radius and 4.5 inches tall to the lid. This leads to a volume of  cubic
inches ...
pretty close to what we found.]
.
So if a 12 oz can of root beer contains 20.65376036 cubic inches of root beer, we can
divide this into the volume of the basketball, and find out how many cans the basketball
can hold. Recall that the volume of the basketball was 433.5259036 cubic inches. Divide
that by 20.65376036 cubic inches per can of root beer, and the answer for the number
of cans of root beer that can be poured into the basketball is:
.
 or about 21 cans of root beer in the
basketball.
.
There are a lot of chances for error in this problem. Recall that we used the outside
dimensions of the basketball to calculate the interior volume. This ignores the fact that
the interior of the basketball will be somewhat smaller because of the thickness of the skin
that forms the ball. Also the NBA basketball is allowed to range in circumference
from 29.5 to 29.75 inches. So its interior volume can vary somewhat from its size and
the thickness of the material that comprises. Add to that that the interior volume of
the basketball is less when the ball is deflated so you can pour root beer into it.
.
Another source of error can come from the fact that we equated ounces of root beer to
ounces of water. This is not likely to be true. A can of root beer will likely sink in water,
indicating that it is denser than water. [However, a can of diet root beer may very well
float because it is likely to be less dense than water.]
.
And finally, the density of water changes slightly with temperature. The temperature
of the water we used makes water its most dense. Warmer than that temperature would
decrease the density.
.
All these variables would make this an interesting science experiment. However, the answer
we came up with is probably pretty close.
.
Check the math above. It's sort of late to be working math problems, and there's a reasonable
chance that an error may have crept in somewhere.
.
Hope this helps you to see your way through the problem.
.
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