# Volume of a solid

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• Jan 24th 2010, 07:20 AM
JJ007
Volume of a solid
Volume of a solid formed when the region bounded by the graphs $\displaystyle y=x^3, y=0, x=1$ is revolved about line x=2.
I don't know where to start. Shell Method?
• Jan 24th 2010, 07:38 AM
skeeter
Quote:

Originally Posted by JJ007
Volume of a solid formed when the region bounded by the graphs $\displaystyle y=x^3, y=0, x=1$ is revolved about line x=2.
I don't know where to start. Shell Method?

shells is one possibility ...

$\displaystyle V = 2\pi \int_a^b r(x) \cdot h(x) \, dx$

sketch your representative rectangle in the described region

$\displaystyle a = 0$

$\displaystyle b = 1$

$\displaystyle r(x) = 2-x$

$\displaystyle h(x) = x^3$
• Jan 26th 2010, 04:39 PM
JJ007
Got it. So for a similar one: $\displaystyle y=x^2, y=4$ revolved about the x-axis would be:
$\displaystyle V=2\pi\int_0^4y[\sqrt{y}-0]dy$ ?

Thanks.
• Jan 26th 2010, 04:51 PM
skeeter
Quote:

Originally Posted by JJ007
Got it. So for a similar one: $\displaystyle y=x^2, y=4$ revolved about the x-axis would be:
$\displaystyle V=2\pi\int_0^4y[\sqrt{y}-0]dy$ ?

Thanks.

if it is only the region in quad I that is rotated, then your integral set up is correct.