Take a cookie dough rolled flat into a perfect circle of radius R, and wrap it around a cylinder of radius R/Pi , such that opposite points of the original circle now meet at the top. After the cookie is baked and hard, remove the cylinder and fill with cream cheese.

Scrape off the excess filling using a straight edge held perpendicular to the long axis and connecting symmetric points of the edges as you scrape.

What is the volume of one of these theoretical cannoli?

(In reply to re: Integrating the other way by Charlie)

I've edited my solution and arrived at about the same conclusion (0.5339r^3) you did but am still hopeful that an explicit solution to that integral exists...

Posted by Eric on 2006-11-01 20:18:51