Thanks a lot I.M and Adam! your guidance has been great!

Oh I see, I think the first assignment method should be good enough for me at this point, although I'll look through the other methods of assignment as well.

I have input arbitrary values into a,b,c and h into the implicitregion equation (with z conditions as: z <= -h && z >= -c).

what could possibly be done to obtain the cutting plane ?

I'm assuming I have to solve for the a and b values of the ellipse equation where z = -h (i.e. at the cutting plane)? In the plot, I have set h = 1

Greetings I.M and Adam

Really appreciate the advice regarding the stated problem. Wow I didnt know the ordering of variables and adding more specific conditions made so much difference in terms of computation time. Thank you for the heads up regarding that.

Also, I'm sorry for this but could I arbitrarily assign values to a,b,c and h in Mathematica to evaluate the expression (a b h (3 c^2 - h^2) [Pi])/(3 c^2)? Say something similar to a user input stored in the variables?

Regards Corse

Hi,

In V10 you can compute it using the built-in Volume function:

In[1]:= reg=ImplicitRegion[x^2/a^2+y^2/b^2+z^2/c^2<=1 && z<=0 && z>=-h,
        {z, y, x}];

In[2]:= Volume[reg, Assumptions->a>0 && b>0 && c>0 && h>0]

                                                       2    2
                    2 a b c Pi               a b h (3 c  - h ) Pi
Out[2]= Piecewise[{{----------, c - h < 0}}, --------------------]
                        3                               2
                                                     3 c

Note that I used the variable order {z, y, x}. Volume computation problems involving symbolic parameters are hard in general and the computation time often depends on variable ordering (that is the order in which we compute the iterated integrals). Here I put the variable z first because it appears in the extra conditions. The result was computed in 6 seconds. With variables ordered {x, y, z} the computation takes about 10 minutes.

Best regards, Adam