Mathematical Problem

A Cooper and Vintner sat down for a talk,
Both being so groggy that neither could walk,
Says Cooper to Vintner, "I'm the first of my Trade,
There's no kind of vessel, but what I have made,
And of any shape Sir - just what you will -
And of any size Sir - from a ton to a gill!"
"Then", says the Vintner, "You're the man for me -
Make me a vessel if we can agree.
The top and the bottom diameter define,
To bear the proportion as 15 to 9,
Thirty-five inches are just what I crave,
No more and no less, in the depth, I will have.
Just thirty-nine gallons this vessel must hold -
Then I'll reward you with silver and gold -
Give me your promise, my honest old friend?"
"I'll make it tomorrow, that you may depend!"
So the next day the Cooper his work to discharge,
Soon made the new vessel, but made it too large,
He took out some staves which made it too small,
And then cursed the vessel, the Vintner and all.
He beat on his breast, "By the Powers", he swore
He never would work at his trade any more.
Now my worthy friends, find out if you can,
The vessel's dimensions, and comfort the man!