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

Surface Area: r 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: Surface Area about x -axis (Cartesian): To rotate about the y -axis, just reverse x and y in the formula!

Example: Rotate about the y -axis.

Example: Rotate about the y -axis.

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

Example: rotated about x -axis. ENTER Y STO

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

Don’t forget to clear the x and y variables when you are done!  ENTER F44 Y X Once again …