Surface Area Worksheet - UH



A.P Calculus Worksheet: Areas of Surfaces of Revolution

Find the areas of the surfaces generated by revolving the curves in problems 1-4 about the axes indicated:

1. [pic], about the [pic]-axis. Check your result with a formula from geometry.

2. [pic], about the [pic]-axis.

3. [pic], about the [pic]-axis.

4. [pic], about the [pic]-axis.

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

5. The surface of a sphere. Use an integral to find the surface area of the sphere generated by revolving the semicircle [pic], [pic], about the [pic]-axis. Check your result with a formula from geometry.

6. The surface of an astroid. Find the area of the surface generated by revolving the portion of the astroid [pic] shown below about the [pic]-axis. (Hint: Revolve the first quadrant portion [pic], [pic], about the [pic]-axis, and double your result.)

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Answers:

1. [pic] 2. [pic] 3. [pic] 4. [pic] 5. [pic] 6. [pic]

-----------------------

[pic]

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download