please solve math portion as I do not understand, i need the dimensions for the tube and then a formula for a small pocket size version as well as the cost of each provided in 2nd screenshot.

007 Math is All You Need James Bond Research Laboratories 3.14159 Mean Street James Bond 007 London, England 12345 MAT 220 Students Chandler-Gilbert Community College 2626 East Pecos Road Chander, AZ 85225 Dear Calculus Creators: As you well know I am the head of 007's Research Laboratory for weapons of mass destruction. Currently, I am faced with a serious situation in which I desperately need your help. I recently discovered a formula for producing a new gas which, if put into the wrong hands, would have disastrous results. The gas, when inhaled, gives a human the ability to float and maneuver about in the air as if flying. By just inhaling a small mount, 00/ would be able to escape an enemy if caught in a desperate situation. Dubbed FIG-MH (Fully Inhalable Gas for Maneuvering Humans. ..pronounced "fig-muh") by my research team, the gas needs to be stored in multiple containers for different purposes. Your enterprising and resourceful professor has indicated that, due to your vast experience in these matters, you will be able to provide valuable assistance. My research team has determined that the best method for storing the FIG-MH should be modeled after the tanks used by the Mesaba Oil and Propane Company in Coleraine, Minnesota (see picture below). MESABA Not only is the design efficient, it will also serve to disguise this valuable commodity. We will use the general shape used by Mesaba...a large cylinder. Your first task is to determine the most efficient way to construct the main storage tank. One interesting characteristic of FIG-MH is that it explodes if more than 7200 cubic feet are contained in one unit. Therefore, we wish to construct a tank, like the one in the picture (assume that the end caps are semi-spherical), The name is Band.. .James Bond 2 Scott Adamson and Trey Cox @2000007 Math is All You Need so that it is as large as we dare make it (you decide if you should allow some margin for error), but as inexpensive as possible. Here are the costs involved: The metal for the sides that is used costs $20.00 per square foot . The metal used for the two semi-spherical end caps cost $35.00 per square foot Since the metal to construct the cylinder comes in 5 pieces (two end caps and three tubes), the pieces must be welded together at a cost of $1.50 per foot (including labor) 3 Steel Tubes As with Mesaba Oil, we will need tanks of similar shape, but smaller volume for a variety of purposes. In fact, we will need to construct a tank small enough for 007 to carry in his pocket for quick access. So, please provide a formula for the dimensions of the general tank of cheapest cost. Be sure to make your report convincing and thorough since it is so difficulty to get money out of the purchasing department! At least, you should include: . The symbolic mathematics performed A verbal explanation of the mathematics performed . Graphs to further explain the mathematics Numerical data for further proof As you know, if any of this information gets into enemy hands or in the unlikely event that you are taken prisoner, you are to disavow any contact with our office and knowledge of this project. I appreciate your prompt response and look forward to your correspondence. It is imperative that I have your report by the deadline of I am confident in your ability to perform this important task. Where would we be without you? God save the Queen! Q P.S. A note from your enterprising and resourceful professor. When generalizing, treat the volume as a constant, V, and find the minimum cost for this general volume tank. You are free to use any technology (computers, graphing calculators) as a tool for problem solving. Just be sure to clearly explain the output. The name is Bond.. .James Bond 3 Scott Adamson and Trey Cox @2000