Question
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)
y=3(2-x), y=0, x=0
y=3(2-x), y=0, x=0
Answers
Reiny
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
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