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It does not assist, since the total volume of coins IS NOT GIVEN.
The given is the volume of the bucket, which is TOTALLY DIFFERENT THING.
Hello, why you want to solve the problem, which is formulated IMPROPERLY ?
For what ? What is your goal ? What do you want to learn from it ?
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What you can do, is to ESTIMATE the maximum number of coins of each type by dividing the total given volume
by the volume of each separate type of coins, assuming that the content is homogeneous.
But not to determine the number of different type of coins in the mixture.
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Also, in your post I see these numbers (in cubic inches)
Nickel; .0438 " "
Dime; .0012 " "
Quarter; .000049 " "
When I compare the volumes of dimes and quarters in your table, I can not believe that these numbers are correct.