Question

Show that the equation of the right branch of the hyperbola in Figure 76 is given by \[ x=g_{2}(y)=\sqrt{a^{2}+by^{2}} \]

where \(a=147\) and \(b=0.16.\)

Question

Find the volume of the solid of revolution obtained by revolving the area enclosed by \(x=g_{2}(y)\) from \(y=-442\) to \(y=123\) about the \(y\)-axis.

Question

Using the fact that the walls are \(0.42\text{ft}\) thick, show that the equation of the interior hyperbola is given by \[ x=g_{1}(y)=\sqrt{q^{2}+ry^{2}} \]

where \(q=146.58\) and \(r=0.16\). See Figure 77.

Question

Find the volume of the solid of revolution obtained by revolving the area enclosed by \(x=g_{1}(y)\) from \(y=-442\) to \(y=123\) about the \(y\)-axis.

Question

Now determine the volume (in cubic feet) of concrete required for the cooling tower.

Question

Do an Internet search to find the cost of concrete. How much will the concrete used in the cooling tower cost?

Question

Write a report for an audience that is not familiar with cooling towers summarizing the findings in Problems 1–6.