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

r Surface Area: Consider a curve rotated about the x-axis: The surface area of this band is: r 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 ENTER

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

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