# Thread: volume of solids of revolution

1. ## volume of solids of revolution

hi, i'm doing a maths assignment on "volume of solids of revolution" and stuck on one particular question. the question asks for the volume of the cross bounded by y=x, y=-x, y=x+2, y=-x+2 and the curve y=x^2-4. it is to be rotated around the y-axis. i really don't know how to do it, neither do my classmates. i had an idea of finding the area of the cross and rotating that but it wouldn't work out.
any ideas?

here is a screenshot of the graph.

2. Didn't I already do this one?

2) Axis of rotation is what?
3) Find the 12 intersections.
4) etc. What did I say before. I don't recall.

3. yea you did, but i have figured it out now. i found the 12 intersections and am rotating around the y-axis. thanks for your help

4. Did you get twice the required answer? It is a common error.

5. not sure as it is a school assignment, but the answer i got is 48.116units^3. looks about right to me.

6. I didn't look at it real closely, but I'm closer to $\displaystyle \frac{68}{3} \pi$, quite a bit more than you managed. I hardly can wait to see your solution.

7. Heres how I went about it:

Just consider one side. You can look at it as two branches. The top branch is still bounded by 3 lines. However, if we cut this area in half aloing the the intersection on the middle/outside, then each side is only two lines bouding the areas. If you follow the same pricinple for the bottomw branch, you will have 4 different areas rotated. The is one little bit of overlap, the triangle shape, but you can easily rotate that and subtract it from the total.