# Prolate spheroid surface area

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Joshua Ustaran-Anderegg on 5 Oct 2022
I am trying to calculate the surface area of a prolate spheroid using matlab. I am using the equations for s and e as stated in the following article https://mathworld.wolfram.com/ProlateSpheroid.html. I already know the value of the polar radius c (25), but am wanting to insert a vector of possible answers for a so that I produce a vector of surface areas s. This is what I have coded so far but only works for individual values of a rather than vectors. Any help would be much appreciated.
function s = surface_area_calculator(c,a)
e = sqrt(c^2 - a^2)/25;
s = (2*pi*a^2) + ((2*pi*a*c)/e)*asin(sqrt(c^2 - a^2)/c));
end

John D'Errico on 5 Oct 2022
You need to learn about the dotted operators, and why they are necessary.
Yuou want to compute an element-wise operation, one that applies to every element of a vector. These are the .*, .^ and ./ operators, as * and * and ^ do different things in MATLQAB when applied to matrices and vectors.
You don't need them when you multiply by a scalar, but be careful, as if you divide a scalar by a vector, you need the dotted operator.
And there are no .+ or .- operators, as they are not needed.
Since a is a vector, this will be sufficient:
e = sqrt(c^2 - a.^2)/25;
s = (2*pi*a.^2) + ((2*pi*a*c)./e)*asin(sqrt(c^2 - a.^2)/c));
See that 2*pi*a*c)/e was acceptable, since 2, pi and c are al assumed scalars. But e is a vector, as is a.
Had you just used the dotted operators through out that function, it would have worked too.
Joshua Ustaran-Anderegg on 5 Oct 2022
Thank you very much

Torsten on 5 Oct 2022
Edited: Torsten on 5 Oct 2022
I calculated the surface area of a sphere of radius 1 which should be 4*pi.
The below formula from WolframAlpha seems to work for prolate spheroids while your implementation fails.
format shortE
c = [1 4 16 55];
a = [1 3 10 32];
s = 2*pi*(a.^2+c.^2.*hypergeom([0.5,1],[1.5],1-c.^2./a.^2))
s = 1×4
1.0e+00 * 1.2566e+01 1.3893e+02 1.7818e+03 1.9349e+04
4*pi
ans =
1.2566e+01
e = sqrt(c.^2 - a.^2)/25;
s = 2*pi*a.^2 + 2*pi*a.*c./e.*asin(sqrt(c.^2 - a.^2)./c)
s = 1×4
1.0e+00 * NaN 5.7146e+02 2.4306e+03 1.2304e+04