The Disk/Washer Method: Axis Of Revolution Question

[carlodelmundo]

Homework Statement

http://65.98.41.146/~grindc/SCREEN01.JPG

Find the volume of the solid generated by evolving the region bounded by y = sqrt(x), y = 0, x = 4, when revolved around the line x = 6

Homework Equations

The Disk/Washer Method -

The Attempt at a Solution

let R(y) = 6 - y^2
r(y) = 2

Okay. What I don't quite understand is why we translate the graph to the right 6 units, and letting the inner radius equal 2. Can anyone shed some light on why we do this? A counter-example would help me understand this easier.

My $0.02... maybe you can clarify it:

By translating the graph y = sqrt(x), 6 units to the left, the vertex point (0,0) now becomes (6,0)... and it's similar, as if, rotated by the y-axis. I know there is a gap of 2 units (from x = 4 and x = 6, as shown by the graph). But where does the subtraction come from?

Carlo

 

[Dick]

The gap of 2 is the distance from x=6 to x=4, which is 6-4. There's a subtraction in there too. Similarly the distance from x=y^2 to x=6 is 6-y^2. Subtracting a larger number from a smaller gives the distance between them.