Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the y-axis. (Use Disc Method)

Question

y=3(2-x), y=0, x=0

Answer 1

y-intercept is 6

y = 6-3x
3x = -y + 6
x = -y/3 + 2
x^2= y^2/9 - 4y/3 + 4

vol = π[integral] y^2/9 - 4y/3 + 4 dy from 0 to 6
= π[ y^3/27 - 2y^2/3 + 4y] from 0 to 6
= π( 8 - 24 + 24 - (0) )
= 8π

better check my arithmetic