Find the volume of solid generated by revolving the region bounded by the curve 𝑦 = √𝑥, 𝑦 = 0, 𝑥 = 2 about the line 𝑦 = 5.
160 visualizaciones (últimos 30 días)
Mostrar comentarios más antiguos
vidya g
el 2 de En. de 2022
Comentada: Nithish
el 17 de En. de 2023
Find the volume of solid generated by revolving the region bounded by the curve 𝑦 = √𝑥, 𝑦 = 0, 𝑥 = 2 about the line 𝑦 = 5.
2 comentarios
Nithish
el 17 de En. de 2023
%Evaluation of Volume of solid of revolution
clear
clc
syms x
f(x)=sqrt(x); % Given function
yr=5; % Axis of revolution y=yr
I=[0,2]; % Interval of integration
a=I(1);b=I(2);
vol=pi*int((yr-f(x))^2,a,b);
disp('Volume of solid of revolution is: ');
disp(vol); % Visualization if solid of revolution
fx=matlabFunction(f);
xv = linspace(a,b,101); % Creates 101 points from a to b
[X,Y,Z] = cylinder(fx(xv)-yr);
Z = a+Z.*(b-a); % Extending the default unit height of the
%cylinder profile to the interval of integration.
surf(Z,Y+yr,X) % Plotting the solid of revolution about y=yr
hold on;
plot([a b],[yr yr],'-r','LineWidth',2); % Plotting the line y=yr
view(22,11); % 3-D graph viewpoint specification
xlabel('X-axis');ylabel('Y-axis');zlabel('Z-axis');
Respuesta aceptada
Image Analyst
el 2 de En. de 2022
Editada: Image Analyst
el 2 de En. de 2022
x = linspace(0, 30, 1000);
y = sqrt(x);
plot(x, y, 'b-');
grid on;
yline(0, 'Color', 'g', 'LineWidth', 2);
yline(5, 'Color', 'g', 'LineWidth', 2);
xline(2, 'Color', 'g', 'LineWidth', 2);
text(5, 4, 'Not this region', 'Color', 'r', 'FontSize', 15)
text(11, 2.5, 'Spin this region', 'Color', 'r', 'FontSize', 15)
You need to actually specify both ends of x.
Is x1=0 and x2=2, or is x1=2 and x2 = 25?
Más respuestas (1)
John D'Errico
el 2 de En. de 2022
Editada: John D'Errico
el 2 de En. de 2022
Ok. I did it. Not too hard. Oh. Wait. Was this YOUR homework assignment, given to you? Is there a reason why we should do it for you?
Please stop posting your homework assignment questions. They were assigned to you, not to us. Unless, of course, you are willing to give us the name and address of your teacher. Then we can send in the solution directly to them, and get credit for ourselves.
Homework is given to teach you. In this case, it would teach you both MATLAB and mathematics, but only if you make an effort. Your brain is a muscle. Exercise it, and it will get stronger.
Note: Had you made an effort, I would have offered help, to a degree proportional to the effort you made. Having shown no effort, I'll tell you only that it took about 20 seconds to write the very few lines of code I used to solve this. (If you count the line syms x y, 3 lines in total.) So in a sense, I did give you help, since I gave you the very first line of code I used.
Ver también
Categorías
Más información sobre 2-D and 3-D Plots en Help Center y File Exchange.
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!