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Volume Calculation: Rotating y=0 Region around y-Axis

Learn how to calculate the volume of a region bounded by y=0 and revolved around the y-axis. Utilize cylindrical shells method for solving in terms of y.

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Volume Calculation: Rotating y=0 Region around y-Axis

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  1. Volumes by Cylindrical Shells

  2. What is the volume of and y=0 revolved around about the y-axis ? - since its revolving about the y-axis, the equation needs to be solved in terms of y - not easy to solve the equation in terms of y

  3. Another Method • Cylindrical shells can be used • Cut into cylindrical sections and solve for the volume of the cylinder • Volume = circumference x height x thickness

  4. Radius is the x position • Δr is Δx or dx • The h is the y position or f(x)

  5. Example Find the volume of the solid obtained by rotating the region bounded by and y=0 about the y-axis

  6. Example • Find the volume of the solid obtained by rotating the region bounded by y = x and y = x2 about the y-axis

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