P. 11 4.Use the substitution u= a2/3–x2/3to find the area of the surface generated when the upper half of the astroid x2/3+ y2/3= a2/3is revolved about the x-axis. 5.Show that the surface area of the torus generated by revolving the circle x2+ (y–a)2= r2, where 0 < r< a, about the x-axis is 4π2ar. 6.Show that the surface area of the zone obtained by slicing a sphere of radius rwith two vertical planes hunits apart is independent of the location of the cutting planes. 7.Let fbe differentiable on [a, b] and suppose that g(x) = f(cx), where c> 0. When the curve y= f(x) on [a, b] is revolved about the x-axis, the resulting surface area is A. Evaluate the integral cbcadxxgcxg//22)()(in terms of Aand c. 8.Suppose fis positive and differentiable on [a, b]. Let Lbe the arc length of fon [a, b] and Sbe the surface area generated by revolving the graph of fon [a, b] about the x-axis. Show that the surface area generated by revolving the graph of y= f(x) + C, where C> 0, about the x-axis is the sum of Sand the surface area of a right circular cylinder of radius Cand height L.