Double Integrals II
Part 2: Balloons at the Fair
Two of your friends have a great money-making opportunity, a balloon concession at the State Fair. They have been offered a choice of two spaces for their balloon booth, both at good locations, and they want to decide which space will enable them to display the most balloons. Since the balloons are filled with helium, height is just as important as floor area. That is, they need to know which space has the larger volume. They know you are a student of calculus, so they ask you to calculate the two volumes for them.
Both booth sites are located within a large circus tent. The tent is symmetrical about a center pole. For the first 3 meters out from the pole, the roof of the tent is flat at a height of 16 meters. Beyond 3 meters out from the pole, the tent slopes down with a height in meters given by
until it reaches the vertical tent wall at a distance of 16 meters from the center. Here is a sketch of the tent.
We will get to the balloon booth sites in the next part of the module. First, as a warmup exercise, calculate the exact volume enclosed by the tent -- no approximations until you convert the answer to decimal form at the end. Think about the best way to go about this before you use your helper application.
