How Do I Find the Volume of a Rotated Solid Using MATLAB?

[[sammich]]

I've been trying to solve one of my MATLAB problems for about 2 weeks now and I am completely lost as to how to solve it. It seems like it would be rather easy to do, but I cannot figure it out.

I have referenced our Calculus 2 textbook, MATLAB textbook, and Google but I'm still stuck.

The problem says:

"The region bounded by the given curves is rotated about the specified axis.
Find the volume of the resulting solid by any method."

x[SUP]2[/SUP]+(y-1)[SUP]2[/SUP]=1

I tried something along the lines of:

syms x y
eq=(x^2)+((y-1)^2)-1

fplot(eq, [0,10])

%a=fzero(eq -blah blah etc- )

but that doesn't work, and even if it did, I don't know where to go from that point.

Can anyone walk me through the steps? This type of problem seems quite important, and I'm worried by the fact that I can't find any help on it. I want to make sure I know how to do it in the future!

Thanks in advance :)

 

[Hepth]

So its a circle with radius 1 from looking at the equation, displaced by 1 along the y axis. Then its rotated around the x axis? Volume = (4/3) pi , the volume of a sphere.

OR integrate it, going to polar coordinates to make it easier.

 

[[sammich]]

Thanks for the response.

I tried solving for y and all, I just can't make it go through.

We are going to have 4/3*pi*r³ evaluated at r=0 and 1, correct? Or am I completely off?

What would I type into MATLAB to assign the volume, integral, etc?

*slams head against keyboard*