Volume of n-sphere? What is wrong with my version?

Hello Experts,

I have to calculate the volume of 10-dim sphere.

Here what I did:

    N = 100000;
    RandVars = -1 + 2*rand(10,N);
    V = zeros(N,1);

    for i = 1:N
        if (sum(RandVars(:,i).^2) < 1)
            V(i) = 1;
        end
    end

    % Mean values using the Monte-Carlo method:
    M = (1/N)*sum(V,1);
    % Error estimation:
    C = V - M*ones(N,1);
    Error = sqrt((1/(N-1))*sum(C.^2,2));

Please have a look what is wrong as I get M = 0.002. Thanks a lot in advance.

[A Jenkins]

duplicate:

http://www.mathworks.com/matlabcentral/answers/105541-volume-of-n-sphere-please-help-me-with-my-version

[Steve]

I have changed my code the question is similar but no one is answering...

Answer 1

[the cyclist]

You forgot to take into account that your bounding hypercube has volume 2^N, not 1, where N is the number of dimensions. (N=10 in your specific case.)