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Math · Calculus
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Draw the curve l_z on the interval [1,10]. Draw a sketch of the figure that would result if this curve is revolved about the x-axis.

Describe the figure that would result if the curve y=\frac{1}{x} on the interval [1,\infty ] were revolved about the x-axis. (This figure is called Gabriel's Horn)

Claim: The volume V of this "horn" is finite while its surface area "S" is infinite. The paradox of these statements is that they say that the horn can be filled with a finite amount of paint, and yet there is not enough paint to paint the inside surface. (Since the curve had no thickness, the walls have no thickness so the inside surface area is the same as the outside surface area)

a. What is the Volume of the horn?

b. Show that the Surface area is infinite.

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