How can i plot it

using spherical coordinates, plot only the part of the sphere z =sqrt(9-x^2-y^2) that lies below the cone z = sqrt(x^2+y^2).

[Rik]

Sounds like you need meshgrid (or ndgrid). What did you try?

[Minh Nguyen]

theta = linspace(0,2*pi,30);
phi   = linspace(0,pi/2,30);
[theta,phi] = meshgrid(theta,phi);
r=3;
[x,y,z] = sph2cart(theta,phi,r);
surf(x,y,z,'FaceAlpha',0.3)
hold on
x = -3:0.2:3 ;   
y = -3:0.2:3 ; 
[x,y] = meshgrid(x,y) ;
z = sqrt(x.^2+y.^2);
surf(x,y,z)

I use this code and i can plot two graph 2 z functions but my teacher asked me to plot only the graph below the cone and i dont know how to do it

Answer 1

[Rik]

You have two surfaces:

theta = linspace(0,2*pi,30);
phi   = linspace(0,pi/2,30);
[theta,phi] = meshgrid(theta,phi);
r = 3;
[x,y] = sph2cart(theta,phi,r);

z_sphere = sqrt(9-x.^2-y.^2);
z_cone = sqrt(x.^2+y.^2);

%remove all complex elements
z_sphere(imag(z_sphere)>eps)=NaN;z_sphere=real(z_sphere);

They share the same coordinate grid, so now we can do element-wise operations. You need to remove points where z_sphere is higher than z_cone. The easiest way to remove points without messing up the coordinate grid is by marking them with NaN:

z_sphere( z_sphere>z_cone ) = NaN;
surf(x,y,z_cone,'FaceAlpha',0.3),hold on % optional line
surf(x,y,z_sphere)
view(45,45)

[Minh Nguyen]

Oh thanks you so much !!!