This script gets the volumes of D-mentional unit sphere by Monte Carlo simulation.

sphere_Monte_Carlo.m

clear

% Number of random data points,case of 100, 1000 & 10000
N = [100,1000,10000];
[~,A] = size(N);
% Dimension numbers
D = 20;

for d = 1:D
    
    for a=1:A
        cnt=0;
        volume = zeros(N(a),1);

        for n = 1:N(a)

            vec = rand(d,1);
            cond = vec'*vec;

            if(cond<=1)
                cnt = cnt + 1;
            end
            % Get volume by Monte Carlo using n data points.
            volume(n,1) = (cnt / n)*2^d;
        end

        % Plot the results
        subplot(A,1,a);plot([1:N(a)], volume);
        xlabel('number of random data point');ylabel('Volume');
        lgnd_vlm = sprintf( 'Volume: %f', volume(N(a)) );
        legend( lgnd_vlm );
     
    end
    
    saveas(gcf,['result' num2str(d) '.fig']);
end