I found this one on the Mc Andrews Univ math web site.
In the version I heard from a calculus teacher at the Air Force Academy, Edison had told him to fill the bulb with water and pour it into a measuring instrument. (Beware children.... Teachers lie)There is an often-told anecdote relating to Upton (Francis Robbins Upton) calculating the volume of a flask. Many versions are rather inaccurate while that by Jehl seems entirely authentic :-I was once with Mr Upton calculating some tables he had put me on, when Mr Edison appeared with a glass bulb having a pear-shaped appearance in his hand. It was the kind we were going to use for our lamp experiments; and Mr Edison asked Mr Upton to please calculate its cubical content in centimetres. Now Mr Upton was a very able mathematician, who after he finished his studies at Princeton went to Germany and got his final gloss under the great master Helmholtz. Whatever he did and worked on was executed in a purely mathematical manner and any Wrangler at Cambridge would have been delighted to see him juggle with integral and differential equations with a dexterity that was surprising. He drew the shape of the bulb exactly on paper, and got the equation of its lines with which he was going to calculate its contents, when Mr Edison again appeared and asked him what it was. He showed Mr Edison the work he had already done on the subject and told him he would very soon finish calculating it. "Why," said Edison, "I would simply take that bulb and fill it with mercury and weigh it; and from the weight of the mercury and its specific gravity, I'll get it in five minutes, and use a lot less mental energy than is necessary in such a fatiguing operation.