Answered Essay: Use matlab to create a program that allows you to see how many spheres it will take to fill a rectangular prism.

Use matlab to create a program that allows you to see how many spheres it will take to fill a rectangular prism.

1.) Create variables for prism length, prism width, prism height, and sphere diameter. These should be values that are input by the user using the matlab input function.

2.) Create a variable which is assigned volume of the rectangular prism.

3.) Create a variable which is assigned volume of the spheres.

4.) Using the most efficient packing possible (assume 74% of the available space is filled by the spheres), find the number of spheres which will fit inside the prism.

Assume that the volume of the prism will be much larger than the volume of the spheres.

Expert Answer

% Matlab program to find how many spheres will fill the rectangular pism

prism_length = input(‘n Enter the length of rectangular prism:’); % input the length of the prism
prism_width = input(‘n Enter the width of rectangular prism:’); % input the width of the prism
prism_height = input(‘n Enter the height of rectangular prism:’); % input the height of the prism
sphere_diameter = input(‘n Enter the diameter of sphere:’); % input the diameter of the sphere
sphere_radius = sphere_diameter/2; % calculating the radius of the sphere
volume_prism = prism_length * prism_width * prism_height; % calculate volume of the prism (length*width*height)
volume_sphere = ((4*22)/(3*7))* (sphere_radius^3); % calculate volume of sphere (4/3(pi*(r^3))). Here pi=22/7

num_of_spheres = volume_prism/volume_sphere; % calculate the number of spheres required
fprintf(‘n Number of spheres to fill the prism=%d’,floor(num_of_spheres)); % using floor function since the total volume of sphere cannot be greater than volume of prism

Output:

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