# Thread: Need a little help starting a shell method problem

1. ## Need a little help starting a shell method problem

I have no idea how to start this problem off. Just looking for a push in the right direction.

Find the capacity of a wine barrel with the shape of a solid that is obtained by revolving the region bounded by the graphs of $\displaystyle x = R - Ky^2, x = 0, y = -h/2$, and $\displaystyle y = h/2$ about the y-axis.

I would assume the shell method would be easiest to use; however, I am probably wrong haha. Anyone got a few tips to get me started?

2. Originally Posted by Poptimus
I have no idea how to start this problem off. Just looking for a push in the right direction.

Find the capacity of a wine barrel with the shape of a solid that is obtained by revolving the region bounded by the graphs of $\displaystyle x = R - Ky^2, x = 0, y = -h/2$, and $\displaystyle y = h/2$ about the y-axis.

I would assume the shell method would be easiest to use; however, I am probably wrong haha. Anyone got a few tips to get me started?
disks w/r to y would be easier, imho.

using symmetry about the x-axis ...

$\displaystyle \displaystyle V = 2\pi \int_0^{\frac{h}{2}} (R-ky^2)^2 \, dy$