Question

Write a MATLAB script using a Monte Carlo method to estimate the volume of a 3-dimensional ball of radius R=0.5.

Answer 1

code:

%number of sample space in first quaradant
k=10^5;
%size of volume
R=0.5;

%random x,y,z co-ordinate
x=rand(k,1)*0.6;
y=rand(k,1)*0.6;
z=rand(k,1)*0.6;

%count total points inside sphere
counter=0;
for i=1:k
if ((x(i)^2+y(i)^2+z(i)^2)<=R^2)
counter=counter+1;
end
end

%volume of the cube containing the sphere
a=0.6;
vol_box=a^3;

%volume of cube calculated using monte carlo
vol_sphere=8*(counter/k)*vol_box;

%actual volume of sphere
true_val=(4/3)*pi*(R^3);

%display result and error
fprintf('Approx volume of ball %.6f\n',vol_sphere);
fprintf('True volume of ball %.6f\n',true_val);
fprintf('Error : %.6f\n',abs(vol_sphere-true_val));

output:

Command Window >>progl Approx volume of ball 0.527334 True volume of Erro 0.003735 ball 0.523599

For any queries comment down below. I will be glad to help you.

If you like this answer please hit the like button. :)