How to sketch the given solid and its condition?

I have the solid bounded by 2x+z=2 and (x-1)^2 + y^2=z. Please someone help me to sketch the given solid.

Answer 1

[Shubham Khatri]

Hello,

Please use the following code to plot the two surfaces

z = @(x,y) (x-1)^2 +y^2; % function handle to anonymous function
fsurf(z)
hold on
z = @(x,y) 2-(2*x)^1 +0*y^2; % function handle to anonymous function
fsurf(z)

You can use different functions to plot a surface. Although the surfaces are not meeting in this case, but you can refer to this answer to connect surfaces to create a solid.

For more information refer to the documentation of fsurf.

Hope it helps

Answer 2

[DGM]

For simple visualization, it's often sufficient to just truncate the surfaces by setting the excess values to NaN.

% plot domain
x = linspace(-1.1,1.1,100);
y = linspace(-1.1,1.1,100).';

z1 = (x-1).^2 + y.^2;
z2 = 2 - 2*x + 0*y; % the zero term is just there to force expansion

% mask off surfaces beyond enclosed volume
m = z1>z2;
z1(m) = NaN; 
z2(m) = NaN;

surf(x,y,z1); hold on
surf(x,y,z2);
shading flat
axis equal
view(10,30)
camlight

This doesn't result in a perfectly closed volume, since the surfaces are rectangular meshes and they aren't joined at the edge. For a fine mesh, the result is sufficient to visualize the volume and typically satisfy the intent of homework assignments. You may choose to opt for different view/shading settings or a more complicated approach entirely.