# Volume by Shell and Washer Methods

## Homework Statement

Find the volume generated by rotating the given region about the given line using the Shell method and the Washer method.

x = 4y [y = x/4], y = 0, x = 0, x = 8 about x

## Homework Equations

V = pi $$\int^b_a$$ ((Rtop2(x) - rbottom2(x))dx

V = 2pi $$\int^d_c$$ (y[f(y)-g(y)])dy

## The Attempt at a Solution

I'm not sure why I can't reconcile these two answers. I'm having some similar problems with more of these exercises but if someone can help me see where I'm going wrong I'm sure I can rework them successfully.

Washer:
V = pi $$\int^8_0$$ ((x/4)2)dx = 32pi/3

Shell:
V = 2pi $$\int^2_0$$ (y(4y))dy = 64pi/3

#### Attachments

• 6.5 KB Views: 351
Last edited:

Related Calculus and Beyond Homework Help News on Phys.org
I forgot about x=8. The shell method should be V = 2pi $$\int^2_0$$ (y(8-(4y)))dy = 32pi/3.

:facepalm:

Double-post :/

:facepalm:

Last edited: