Question

A forus is shaped like a doughnut. If its inner radius isa and its outer radius is b, its volume and surface area are given by V '(a + b(b - a)? A = (b2 - ) a. Create a user-defined function that computes V and A from the arguments a and b. LastName_FirstName_P4_fn_calc. b. Test for values where acb, ab and aub. Use values between 1 and 10 for a and b. Your output should show a, b, V and A. c. Suppose that the outer radius is constrained to be 2 in. greater than the inner radius. Write a script file that uses your user-function to plot A and V verses a for 0.25 <= 0 <= 4.00 in. Your plot should resemble this one. File Et View Insert Tools Desktop Window Help Volume and Surface Area of a Torus 1300 1200 1100 Volume and Surface Area 500 400 0 0.5 1 1.5 3 3.5 4. 2 2.5 Inner radius
Matlab

Answer 1

% Matlab file : P4_fn_calc.m

function [V,A] = P4_fn_calc(a,b)
% Matlab function P4_fn_calc to calculate the volume and surface area
% of a torus gicen its inner radius, a and outer radius,b
  
V = (((pi.^2)./4).*((a+b).*((b-a).^2)));
A = (pi.^2).*((b.^2) - (a.^2));
end

%end of Matlab function

% Matlab file P4.m
% Matlab main script to calculate the values for Volume and Surface area
% for the values of a < b, a>b and a = b using values of a between 1 and 10.
% a < b
a = 2;
b = 4;

[V,A] = torus(a,b);
fprintf('a = %f b = %f V = %f A = %f\n',a,b,V,A);

% a > b
a = 4;
b = 2;

[V,A] = torus(a,b);
fprintf('a = %f b = %f V = %f A = %f\n',a,b,V,A);

% a = b
a = 2;
b = 2;

[V,A] = torus(a,b);
fprintf('a = %f b = %f V = %f A = %f\n',a,b,V,A);
% generate a plot of Volume and Surface Area vs inner radius
% generate 100 points between 0.25 and 4 for the inner radius
a = linspace(0.25,4,100);
b = a+2; % outer radius is 2 in greater than inner radius
% calculate volume and surface arae
[V,A] = torus(a,b);
% plot the graph
plot(a,V,'r-');
hold on;
plot(a,A,'b-');
hold off;
title('Volume and Surface Area of a Torus');
xlabel('Inner radius');
ylabel('Volume and surface Area');
legend('Volume','Surface Area');
%end of script

Output:

a = 2.000000 b = 4.000000 V = 59.217626 A = 118.435253 a = 4.000000 b = 2.000000 V = 59.217626 A = -118.435253 a = 2.000000 b = 2.000000 V = 0.000000 A = 0.000000 Figure 1 Eile Edit View Insert Tools Desktop Window Help dalah @ 08 0 Volume and Surface Area of a Torus 200 - - Volume -Surface Area Volume and surface Area O 0.5 1 1.5 2 2.5 Inner radius 3 3.5 4