# If R is the area enclosed by f(x) and g(x), is the volume of the solid generated by revolving R around the x-axis then revolving that solid around the y-axis equal to the volume of the solid generated if the order of the revolutions was switched?

Jan 9, 2017

No

#### Explanation:

Apart from the fact that the formulas are different

$V = {\int}_{x = a}^{x = b} \pi {y}^{2} \mathrm{dx}$
$V = {\int}_{y = a}^{y = b} \pi {x}^{2} \mathrm{dy}$

A factor is proximity to the axis of rotation, so if if you think about it intuitively, and consider a small area near $x = 50$ and rotated around the $x$-axis it would produce a small shape with a small volume. But rotated around the y-axis it would product a large object (because it is relatively far away form the y-axis) and much larger volume