
Grarnold Smurfenegger |

Well, it floats, so it must weigh the same as a duck or witch, right?
Is this question on the Citizenship Exam?
If you knew how much wood went into the cask, then this might help.

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A typical modern day Bordeaux-style barrel holds 225L (about 1/4 tun) and weighs about 120 lbs. A wine barrel is approximately 3 feet tall and about 2 feet in diameter, leading to a surface area of about 25.13 square feet. Thus, the weight of oak used in barrelmaking has an approximate density of 4.8 pounds per square foot.
So, what does a tun look like? If we assume a cask as a cylinder 3 feet in diameter, then it has to be about 5 feet long to hold the volume. The total surface area of such a cylinder is 61.26 square feet. Assuming the same density, that's 294.1 lbs.
So an empty tun is about 300 lbs.

Ambrosia Slaad |

A typical ("hogshead") barrel seems to hold 52-60 gallons of water/wine and weighs between 150-200 lbs.
A tun holds 252 gallons of water/wine -- roughly four hogsheads -- so I'd guesstimate it's thicker/reinforced construction to be at least 800 lbs (minus some if it is open on one end, plus some if it has absorbed some of the wine aging in it). I imagine this is roughly in the ballpark, at least until someone else comes up with a better answer.
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Better answer: Is there a local winery you can call and ask?
If you find out, I'd love to know how much it really weighs.
Edit: Ninja'd by the Wino. But I think 300 lbs. is way too light.