find the volume of the solid generated by revolving the region enclosed by the triangle with vertices (3,0) (3,4) and (5,4) about the y axis?

Let A = (3,0) , B = (3,4) , C = (5,4) , and
L is the line passes through A and C
M is the line passes through A and B

Then the eq. of M is x = 3
and the eq. of L is y = 2x - 6 , so x = y/2 + 3

By Washer Method,
V = ∫ π ( R^2 - r^2 ) dy
R = outer radius = d( L , y-axis ) = y/2 + 3
r = inner radius = d( M , y-axis ) = 3

V
= ∫ π ( R^2 - r^2 ) dy , from y=0 to y=4
= π * ∫ [ (y/2 + 3)^2 - 3^2 ] dy
= π * ∫ [ (y^2)/4 + 3y ] dy
= π * [ (y^3)/12 + (3/2)y^2 ] , from y=0 to y=4
= π * [ (4^3)/12 + (3/2)4^2 ]
= 88π / 3 ... Ans