Dear all,(adsbygoogle = window.adsbygoogle || []).push({});

I do really need your help.

I'd like to find the volume contained between a sphere (x^2+y^2+z^2=r^2) , plane1 (ax+by+cz+d=0), and plane2 (z-h=0).

Would you please check what I've done till now?

From the sphere and plane1 equations I got:

x1=sqrt*(r^2-y^2-z^2)

x2=d/a-(b/a)y-(c/a)z

Then, by assuming that x1=x2 (as the sphere and plane1 intersect), I derived two equations: one for y1 and one for y2 as follow:

y1=f(z)

y2=g(z)

Also, by assuming y1=y2, I got:

z1=M (a constant value)

z2=N (a constant value)

Now, let assume z1<h<z2

So, to derive the volume I thought that I can run three integrals as bellow:

A=int(1,x,x1..x2)

B=int(A,y,y1..y2)

volume = int(B,z,h..z2)

Am I right? Would you please let me know that what I am doing is right or not?

I also drew a simple picture. The shaded area represents the portion of the sphere that I am looking for its volume.

Thanks in advance,

Nejla

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# Volume between three surfaces

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