Revolving Regions: Double check my work...

[daneeyah]

The question asks:

Let R be the region bounded by y=x^2 and y=4. Compute the volume of the solid formed by revolving R about y=4.

The possible answers are:

A) 256pi/21
B) 512pi/15
C) 2pi
D) 8pi

My answer for this question that I got was D..
Am I right? If not, please explain why. :|


The second question is basically the same (and the same options), except instead of revolving R about y=4, we are revolving R about x=0...
For that case, I got C.


Thanks again for your help! :wink:

 

[Deleted member 4993]

The question asks:

Let R be the region bounded by y=x^2 and y=4. Compute the volume of the solid formed by revolving R about y=4.

The possible answers are:

A) 256pi/21
B) 512pi/15
C) 2pi
D) 8pi

My answer for this question that I got was D..
Am I right? If not, please explain why. :| <<<<< Don't know .... show your work so that we can check


The second question is basically the same (and the same options), except instead of revolving R about y=4, we are revolving R about x=0...
For that case, I got C.


Thanks again for your help! :wink:

 

[galactus]

Look at the first one again. I will tell you it is not D.

You can use shells:

\(\displaystyle 2{\pi}\int_{0}^{4}(4-y)\sqrt{y}dy\)

or washers:

\(\displaystyle {\pi}\int_{0}^{2}(4-x^{2})^{2}dx\)

 

[Deleted member 4993]

Look at the first one again. I will tell you it is not D.

You can use shells:

\(\displaystyle 2{\pi}\int_{0}^{4}(4-y)\sqrt{y}dy\)

or washers:

\(\displaystyle {\pi}\int_{0}^{2}(4-x^{2})^{2}dx\)

I think the limit should be -2 to +2 or 2*(0 to 2) for the disks - and correspondingly for washers.