# Find the volume between y=-2x + 4, x-axis, x=1, about the line x=1. Check my work?

1. Jan 18, 2013

### Lo.Lee.Ta.

Find the volume between y=-2x + 4, x-axis, x=1, about the line x=1. Check my work? :)

Hi, everyone.

1. Find the volume of the region between y= -2x + 4, x-axis, x=1, about the line x=1.

I tried to post this before, but I don't think it went through!

2. Alright, so I first drew it out, and the shape is a cone.
Since it revolves around a y-axis, the limits should be also in terms of y.
Every cross-section is a circle.

So this is how I wrote it out:

∫0 to 4 of ∏[((-y/2) + 1)^2]dy

∫0 to 4 of ∏[(y^2/4) -y + 1]

= 1/4 * (y^3)/3) - (y^2)/2) + x |0 to 4

= ((y^3)/12) - 1/2(y^2) + x |0 to 4

= ((4)^3)/3 - 1/2(4)^2 + 4 -(0)

= 64/12 - 8 + 4

= 1.33 or 4/3

So... Is that right?
Thank you so much for checking my work! :)

2. Jan 18, 2013

### Staff: Mentor

Re: Find the volume between y=-2x + 4, x-axis, x=1, about the line x=1. Check my work

What is the exact problem statement? What you have is confusing. Is the region bounded by y = -2x + 4, the x-axis, and the line x = 1 revolved about some line? You don't mention the word "revolved" in your problem statement.

Is the region revolved about the line x = 1 or about the y-axis (the line x = 0)?

3. Jan 18, 2013

### Lo.Lee.Ta.

Re: Find the volume between y=-2x + 4, x-axis, x=1, about the line x=1. Check my work

Yes, it is revolved about the line x=1.

4. Jan 18, 2013

### HallsofIvy

Staff Emeritus
Re: Find the volume between y=-2x + 4, x-axis, x=1, about the line x=1. Check my work

5. Jan 20, 2013

### Lo.Lee.Ta.

Re: Find the volume between y=-2x + 4, x-axis, x=1, about the line x=1. Check my work

Thanks for checking it! :)

I made a lot of mistakes in my work, but I managed to get the right answer! I'll have to fix those!