(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I need to find the volume of the solid generated by revolving this region bounded by the curves about the x-axis.

y = sqrt(x), x+y=6, y=1

2. Relevant equations

3. The attempt at a solution

I find the intersections of these curves I get:

(1,1), (4,2), (5,1)..

Then I see that to get the area of this cross section I need to do two sections from x = 1 to x = 4, and x = 4 to x = 5 if I integrated in terms of x..

So I see that it will be easier to integrate in terms of y:

I will get the area to be

[tex]

A(y) = \int_{1}^{2} [(-y+6)-(y^2)]dy

[/tex]

But now I am confused as to how I can formulate the integral to find the volume of this by revolving around the x-axis?

I know I need to use the difference of the boundary as the radius then multiply by pi.. but I don't understand how to do that if I wrote the area in terms of y?

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Volumn by cross sections - solving in terms of which axis confusion?

**Physics Forums | Science Articles, Homework Help, Discussion**