# Help on a rather easy volume problem

• December 8th 2009, 12:52 PM
Arturo_026
Help on a rather easy volume problem
The problems is to find the volume of the genrated solid when rotated about the y-axis:

$y=x^3 + 1$ $x=0$ and $y=2$

Here is the thing though. I did this exercise using disks and got ~.5 , then I checked the answer in the back and was different, then I used shells and got the right answer. However, I've been going back to the disk method and cannot seems to find my error and keep getting the same asnwer.
Anyone want to see if they get ~1.88 using the disks method.
• December 8th 2009, 01:04 PM
tonio
Quote:

Originally Posted by Arturo_026
The problems is to find the volume of the genrated solid when rotated about the y-axis:

$y=x^3 + 1$ $x=0$ and $y=2$

Here is the thing though. I did this exercise using disks and got ~.5 , then I checked the answer in the back and was different, then I used shells and got the right answer. However, I've been going back to the disk method and cannot seems to find my error and keep getting the same asnwer.
Anyone want to see if they get ~1.88 using the disks method.

$y=x^3+1\Longleftrightarrow x=\sqrt[3]{y-1}\Longrightarrow$ evaluate $\pi\!\!\int\limits_1^2(x-1)^{2\slash 3}dx=\frac{3\pi}{5}\approx 1.8849556$

Tonio
• December 8th 2009, 01:13 PM
Arturo_026
Quote:

Originally Posted by tonio
$y=x^3+1\Longleftrightarrow x=\sqrt[3]{y-1}\Longrightarrow$ evaluate $\pi\!\!\int\limits_1^2(x-1)^{2\slash 3}dx=\frac{3\pi}{5}\approx 1.8849556$

Tonio

Amazing, I just realize that I was solving the problem using the equations of the problem just above it.