Houdini had his feet shackled to the top of a concrete block which was placed in the bottom of a giant laboratory flask. The cross-sectional radius of the flask, measured in feet, was given as a function of height z from the ground by the formula 10 r(2) Vz with the bottom of the flask on a platform one foot off the ground (at z = 1 foot) and the top 11 feet off the ground. The flask was then filled with water at a constant rate of 22ft cubic feet per minute. Houdini's job was to escape the shackles before he was drowned by the rising water in the flask. Part 2: Houdini would like to be able to perform this trick with any flask, using the same concrete block. Help him plan his next trick by designing a flask with cross sectional radius r(2), a function of z created by your group. The flask design will come from a curve that you determine. This curve is then rotated around a line, thus forming a surface. It will probably be easiest to conceptualize your curve as a function of x, and then rotate this curve around the x-axis. Assume the flask will still be filled with water at a constant rate of 22 cubic feet per minute and recall that it takes Houdini 10 minutes to escape. He still wants the dramatic impact of escaping just as the water reaches the top of his head. Show the volume of water in your new flask is correct at the appropriate time. Flask requirements: Your radius function cannot be a multiple of the function given in this project. Your radius function cannot be a linear function (so your flask can't be a cylinder or truncated cone). Like the flask described in this project, yours may sit on a platform so that you don't have to start at z = 0. Houdini needs to be able to get into the flask (i.e., you wouldn't want to have any point where the radius is too close to zero). State the total height of your new flask and give its total volume. Include a computer generated drawing of the flask you create