Using theMatLab Monte Carlo method for volume of CN tower

[Eng_physicist]

Homework Statement

I have to do a monte carlo approximation for the Volume of the CN tower for my assignment
but I don't know what size to make the cubes and for the part below the main pod I do not know how to create a tapered tower for loop that gets smaller with each loop so that the coordinates stay with in the triangle any help would be good this is what I have so far

Homework Equations

V=h*pi*(r)^2

The Attempt at a Solution

This the code my proff gave us(which has some of the dimension and he gave us the random coordinate generator plus the if statement for the pod, the rest is mine) to start plus my own modification I having trouble knowing if I did the monte carlo method correctly

height =553.33;
heightroof=457.2;
tapoured_height=342;

base_diameter=66.6;
pod_baseh=200;
pod_toph=250;
n_trials=1e4;
counter=0;
Vpod=0;% volume pod
Vtaop=0;%volume tapered tower
vc=(1/n_trials)^3; %volume of cube
base_tapered=66.6;
coords=rand(n_trials,3);
coords(:,3)=coords(:,3)*height;%scale z coordinates
coords(:,1:2)=(coords(:,1:2)-.5)*pod_diametere;%scale z coordinates
known_volume=height*(base_diametere^2)/4;
%loop to check points
for i=1:n_trials;
%for pod
if coords(i,3)>pod_baseh && coords(i,3)<pod_toph
if sqrt(coords(i,1))^2 +(coords(i,2))^2<(pod_diameter/2)
counter=counter+1;

Vpod = Vpod+ sum(vc);
end

else
%for tapered tower
%%code to check if coords falls with in tapoured tower
if coords(i,3)>0 && coords(i,3)<tapoured_height
if sqrt(coords(i,1))^2 +(coords(i,2))^2<(base_tapered/2)
base_tapered = ( base_tapered)/n_trials;

Vtap = Vtap+ sum(vc);
end

end
end
end
V=Vpod+Vtap; % volume total

 

[KataKoniK]

approx_volume=V*known_volume; %monte carlo approximation


Hello there,

It looks like you have a good start on your Monte Carlo approximation for the volume of the CN tower. Your code seems to be following the correct steps and using the appropriate equations. However, there are a few things that could be improved upon to make your code more accurate and efficient.

Firstly, for the tapered tower, instead of creating a loop to check if each coordinate falls within the tower, you can use a mathematical equation to define the shape of the tower and then check if each coordinate falls within that equation. This will make your code more efficient and accurate.

Secondly, for the cubes, it would be best to make them smaller than the diameter of the base of the tower. This will allow for a more accurate approximation of the volume.

Lastly, instead of using a fixed number of trials (n_trials), it would be better to use a variable that can be adjusted for different levels of accuracy. This way, you can run your code multiple times with different values of n_trials to see how it affects the accuracy of your approximation.

I hope this helps and good luck with your assignment!