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?

1 Answer
Jan 9, 2017



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