What is the volume of a cylindrical wine barrel with a bung hole?

[blakjack]

Homework Statement

A wine barrel has a hole in the middle of its side called a bung hole. To determine the volume of the wine in the barrel, a bung rod is inserted in the hole until it hits the lower seam.
You should make the following assumptions:
-The barrel is cylindrical
-The bung hole is centered along the length of the barrel
-The distance from the bung hole to the corner is d
-The ratio of the length to the diameter of the barrel is t.
Answer the following questions:
You should show that the volume of the cylindrical barrel is V=2(pi)d^3t(4+t^2)^(-3/2)

I don't know how to arrive at the fact that the volume would be what is shown.

Homework Equations

V = pi r^2 h

The Attempt at a Solution

I set the two equations next to each other and tried to see what canceled out which was pi.

So r ^ 2 h = 2(d^3t)(4+t^2)^(-3/2)

Then I got stuck and help would be greatly appreciated.

 

[NateTG]

I think you're missing something, since there's no indication anywhere of what $t$ represents.