Find volume using disk/washer/shell method

[kari82]

Find volume of the solid generated revolving the region bounded by the graphs of the equations about line x=5

y=x, y=0, y=4, x=5

My plan is to use washer method. V=pi∫R(y)^2-r(y)^2 dy from y=0 and y=4

Im having trouble finding the equations for R and r. Can someone please explain me what would be a way to find those equations? Thanks!

 

[Mark44]

Find volume of the solid generated revolving the region bounded by the graphs of the equations about line x=5

y=x, y=0, y=4, x=5

My plan is to use washer method. V=pi∫R(y)^2-r(y)^2 dy from y=0 and y=4

Im having trouble finding the equations for R and r. Can someone please explain me what would be a way to find those equations? Thanks!

Have you drawn a sketch of the region being revolved? The typical area element is a trapezoid whose left edge is along the line y = x and whose right edge is along the line x = 5.

 

[kari82]

yes, i did... and the book says that R=5-y and r=0.. but I can't see why r=0..

 

[kari82]

I think I got it.. r=0 because when it rotates along x=5 there is no inner radius?

 

[Mark44]

Both radii are calculated as distances from the line x = 5. The large radius, R, is 5 - y. The small radius is 5 - 5 = 0. IOW, all of the disks have a radius of 5 - y. Does that make sense?

 

[kari82]

Yes! Thank you so much!