Method of cylindrical shells Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the specified axis.
$y=32-x^2, \ y=x^2$ about the line $x=4$ 
My confusion is that what will be the radius 'x' of cylinder shells which we have to put in the integral.


Cylindrical shell: consider the volume element
$$ dV = 2 \pi h\,dr = 2\pi\,2y\,dx = 4\pi\,x^2dx
$$
Then integrate
$$ V = \int_{x=-4}^4 dV = 4\pi \int_{-4}^4 x^2dx
$$
Cylindrical disk: Cut your solid in half so that you only have to consider the bottom part. Then integrate the volume element
$$ dV = \pi x^2 dy = \pi (2\sqrt{y})^2 dy
$$
$$V = \int_{y=0}^{16} dV = 4\pi \int_0^{16} y\,dy
$$
