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7.4 Day 2 Surface Area

Learn how to calculate the surface area when a curve is rotated about the y-axis. Includes step-by-step examples and helpful formulas.

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7.4 Day 2 Surface Area

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  1. 7.4 Day 2 Surface Area (Photo not taken by Vickie Kelly) Greg Kelly, Hanford High School, Richland, Washington

  2. r Surface Area about x-axis (Cartesian): To rotate about the y-axis, just reverse x and y in the formula! Surface Area: Consider a curve rotated about the x-axis: The surface area of this band is: The radius is the y-value of the function, so the whole area is given by: This is the same ds that we had in the “length of curve” formula, so the formula becomes:

  3. Example: Rotate about the y-axis.

  4. Example: Rotate about the y-axis.

  5. From geometry: Example: Rotate about the y-axis.

  6. Y ENTER ENTER STO rotated about x-axis. Example:

  7. Y ENTER ENTER STO Check: rotated about x-axis. Example:

  8. Y X F4 ENTER Don’t forget to clear the x and y variables when you are done! Once again … 4 p

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