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5053 -Volume by Shells

5053 -Volume by Shells. AP Calculus. Volume by Shells. V = l * w * h ( 2  r * x * f (x). Formula:. Region may be either adjacent to or separate from the axis of rotation. Representative Rectangle is Parallel to the axis of rotation.

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5053 -Volume by Shells

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  1. 5053 -Volume by Shells AP Calculus

  2. Volume by Shells V = l * w * h ( 2  r * x * f (x)

  3. Formula: Region may be either adjacent to or separate from the axis of rotation. Representative Rectangle is Parallel to the axis of rotation. “Parallel therefore shell.”

  4. Formula: Then formula is built on the surface area of a cylinder …. times …. its thickness. r = the distance from the axis of rotation. h = difference between the curves ( n )

  5. r and h Perpendicular to x - axis

  6. r and h Perpendicular to y - axis

  7. Volume by Shells V = l * w * h ( 2  r * x * f (x) a) ||  shell b) c) r = ( x - 0) d) h = (f (x) - 0)

  8. Example: Revolve the region about the y – axis. 1

  9. Example: Rotated about x = 2

  10. Example: Rotated about x = 3

  11. Example: Rotated about y = 8

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