Thread: Need help with finding a volume of revolution with Cylindrical Shells method

y=2-0.5x, y=0, x=1, x=2, rotate about the x axis.
I know that it will be easier to solve it with the regular method, but I need it with cylindrical shell.
I cannot find the radius and the height.
The final answer is 19pi/12
Thanx

Originally Posted by shaharg

y=2-0.5x, y=0, x=1, x=2, rotate about the x axis.
I know that it will be easier to solve it with the regular method, but I need it with cylindrical shell.
I cannot find the radius and the height.

If you must use the shell method, you will need to set up two integrals: one for in which the height of each shell is simply 1, and then another for in which the height of each shell is

Originally Posted by Reckoner

If you must use the shell method, you will need to set up two integrals: one for in which the height of each shell is simply 1, and then another for in which the height of each shell is

So, what is the radius and what is the height?

Originally Posted by shaharg

So, what is the radius and what is the height?

I suggest drawing a picture. The average radius of each shell is the distance from the axis of rotation to each given -value. Since the axis of rotation is simply the -axis, this distance is given by The "height" of each shell (horizontal distance from side to side) I have explained in my previous post. It should be clear from looking at a picture.

Thank You