Consider the shape formed by rotating the line y = 1/x on the interval [1, infinity) about the x axis. If you had such a "horn," would more paint be required to fill the horn or to cover its inside surface? (We are assuming an "ideal" paint whose molecules have an infinitesimal size.) Consider whether the volume of the horn is finite and whether the surface area is finite. Does this result seem intuitively valid? Do you think that we could really create an object and a paint which would demonstrate this mathematical result? Why or why not?

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