A ceramic bowl is turned on a potter's wheel to approximate the surface obtained by revolving the curve y= (2/3)((x^2) - 1 ) from x=1 to x=2 about the y axis. What is the approximate outside area of the bowl? [assume that each unit on the x and y axes represents 10 cm]
Any thoughts?
I'd really appreciate any help, especially if it would lead to the solution.
Thanks.
represents the distance between the curve and the axis of revolution at a given -value. Since we are revolving the curve about the -axis, that distance is just If we were revolving about the -axis, then you would be correct: the distance from the curve to the axis would be
So if we were revolving about the -axis, the area of the surface would be
Consider another example, let's say we wanted to revolve the curve about the line x = 3. Then the distance from the curve to the axis of revolution would be and the area would be
Give me a second and I'll make a picture to help you visualize it.
Please click the thumbnail below for a larger version.
The graph shows the curve along with the three different axes of revolution that I mentioned in my last post. The distance between the point and each axis of revolution is also depicted. The problem that you posted involved revolution about the line (that is, the -axis), which is shown in red.
Sorry for the notational confusion. I should have explained the formula I was using more clearly.