# How do you find the volume of the solid obtained by rotating the region bounded by the curves #y^2=4x#, #x=0# and #y=4# about the y axis?

##### 1 Answer

Feb 16, 2016

#### Explanation:

The graph (before rotation) is shown below

graph{sqrt(4x) [-0.5, 4.5, -0.5, 4.5]}

Slice the solid generated in a manner that is normal to the

Each slice has volume of

#"d"V = pi y^2 "d"x#

#= 4pix "d"x#

The total volume is given by

#int_0^4 4pix "d"x = [2pix^2]_0^4#

#=32pi#