# Thread: Volume of a solid

1. ## 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?

2. 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

$\displaystyle a = 0$

$\displaystyle b = 1$

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

$\displaystyle h(x) = x^3$

3. 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.

4. 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.