# How do you find the volume of the solid obtained by rotating the region bounded by the curves #y = x^3#, #x=0#, and #x=1# rotated around the #y=-2#?

##### 1 Answer

Apr 18, 2016

The region to be rotated about y=-2 is shown here shaded in red.

Consider an element of length y and width

Required volume is that of the annular region

=

The volume of the solid formed by the whole region would therefore be

Integral to solve would be

=

=