Question

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?

Answer 1

No

Explanation:

Apart from the fact that the formulas are different

`V =int_(x=a)^(x=b) pi y^2 dx`
`V =int_(y=a)^(y=b) pi x^2 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