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

2. 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!

3. Example:
Rotate about the y-axis.

4. Example:
Rotate about the y-axis.

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

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

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

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