Graphing cylinders on same axis

I'm trying to graph these two cylinders on the same axis and then draw the cross section of the region bounded by them,but I'm not sure I'm doing it right. The end goal is to choose an order of integration based on the results of the first part and compute the volume of the region.

syms x y z
cyl = x^2 + y^2 - 1;
cyl2 = x^2 + z^2 - 1;
fimplicit(cyl), hold on
fimplicit(cyl2)

Answer 1

[Sam Chak]

Hi @Ikenna Iwudike

Can you try using this code to show your how your cylinders look like? Then we see the region that you want to find the volume.

r = 1;      % radius
n = 200;   
[X, Y, Z] = cylinder(r, n);
h = 2;      % height
Z = h*Z;
surf(X, Y, Z, 'facecolor', [179/255, 205/255, 227/255], 'LineStyle', 'none')
hold on
fill3(X(2,:), Y(2,:), Z(2,:), [251/255, 180/255, 174/255], 'LineStyle', 'none');     % top
fill3(X(1,:), Y(1,:), Z(1,:), [204/255, 235/255, 197/255], 'LineStyle', 'none');     % bottom
hold off
axis square