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#### Yuuki

##### Member
i notice i have much problem solving questions regarding surface areas and volumes of rotation.
it's not so much the setting up of the integration but i can't do the computing.

can you guys suggest online practice problems to do integration required in these kinds of problems??

thanks

#### MarkFL

Staff member

i notice i have much problem solving questions regarding surface areas and volumes of rotation.
it's not so much the setting up of the integration but i can't do the computing.

can you guys suggest online practice problems to do integration required in these kinds of problems??

thanks
Do a search here on the word "revolution" and you will see many worked problems concerning solids and surfaces of revolution.

You could use these problems as practice problems and then compare your results with those posted.

#### SuperSonic4

##### Well-known member
MHB Math Helper
VBulletin search software isn't always that good so you can use google to search this site by adding site:http://mathhelpboards.com to your search

#### Deveno

##### Well-known member
MHB Math Scholar
Here's one to get you started:

Find the volume of the solid of revolution of the region bounded by:

$f(x) = \sqrt{r^2 - x^2}$

and the $x$-axis, rotated about the $x$-axis.

Do the disk method first, then the shell method. One will be lots easier.

(Hint: for the shell method, note that the solid obtained is the same one we obtain by taking twice the volume of the solid obtained by rotating the area bounded by:

$f(x) = \sqrt{r^2 - x^2}$, the $x$-axis, and the $y$-axis about the $y$-axis.

This allows you to integrate over $x$ instead of over $y$).

The "answer" to this problem is well-known and thus it should be easy for you to check your work.