Calculus: Integrals: Applications – #13743

Question: Suppose the graph of y= -1/x from x=0 to x=1is rotated about the y-axis to form an infinitely deep vase.

a) Show that a vertical cross section along the y-axis will have an infinite area. What does this imply about the total surface area of the vase?

b) Show that the vase could be completely filled with a finite volume of water. What is that finite volume?