Washer Method (understanding)

[kpx001]

Hi, im having a little trouble finding the R and r in the washer method
For the problem
y=x, y=0, y=4, x=6 rotating on x=6

i dont know what the R or r is.
R is the farthest function - axis
r is the closest function - axis
if this is true both are the same function? im confused with this problem

 

[stapel]

If the two values were the same, then the volume would be zero, since of course there would be no "thickness" to any of the washers. So that doesn't seem productive....

What did you see when you drew the picture? :wink:

Eliz.

 

[kpx001]

trapezoid rotating on an axis thingy, im confused though
R = 6-y
and r = ???(6) im confused at this drawing to understand the concept.
based on the solution its a disk method problem because theres no hole however.

 

[stapel]

Washers are just circles (radius R) with circular holes (radius r) in the middle. Is this perhaps a case where the inner "circle" has radius r = 0...? :wink:

Eliz.

 

[soroban]

Hello, kpx001!

Did you make a sketch?
This is not a Washer problem . . . It is a Disk problem.

\(\displaystyle \text{Region: }\;y \,=\,x,\;y\,=\,0,\;y\,=\,4,\;x\,=\,6\;\;\text{ revolved about }x\,=\,6\)

        |
       4+         * * * * *
        |       *         *
        |     *           *
        |   *             *
        | *               *
    - - * * * * * * * * * * - -
        |                 6

\(\displaystyle \text{If you're using Disks, the integral is: }\;V \;=\;\pi\int^4_0 R^2\,dy\)
. . \(\displaystyle \text{where }R \:=\:6-y\)

 

[kpx001]

oo i see it, but im sorta confused with that box thing books usually draw to see whether or not its dy or dx... i can now see why r = 0 but can u sortof explain what the outside part represents?

       |
       4+         * * * * *
        |   r   * ====*
        |     *   R       *
        |   *             *
        | *               *
    - - * * * * * * * * * * - -
        |                 6

this is how i viewed it

 

[galactus]

Here's an animated diagram of your region. I believe you'll want to disregard the triangle section at the top.