Cooling Tower Problem: Cooling towers for some power plants are made in the shape of
Chapter 8, Problem 24(choose chapter or problem)
Cooling Tower Problem: Cooling towers for some power plants are made in the shape of hyperboloids of one sheet (see the photograph). This shape is chosen because it uses all straight reinforcing rods. A framework is constructed, then concrete is applied to form a relatively thin shell that is quite strong, yet has no structure inside to get in the way. In this problem you will find the area of such a cooling tower.The cooling tower shown in Figure 8-6l isformed by rotating about the y-axis thehyperbola with the parametric equationsx = 35 sec t y = 100 + 80 tan twhere x and y are in feet.Figure 8-6la. The hyperbola starts at y = 0. What is theradius of the hyperboloid at its bottom?b. The hyperbola stops where t = 0.5. What isthe radius at the top of the hyperboloid?How tall is the cooling tower?c. What is the radius of the cooling tower at itsnarrowest? How high up is this narrowestpoint located?d. Find the surface area of the hyperboloid.e. The walls of the cooling tower are to be 4 in.thick. Approximately how many cubic yardsof concrete will be needed to build thetower?
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