Cylinder: the radius is r, the height is 2H, and the radius of the circumscribed sphere is R=(r square +H square) square, for example, r = 3 and h = 5.

Then R=5.

Cone: The vertex angle of the cone is 2α, the generatrix is 2L, and the circumscribed sphere radius R=L/cosα.

Cuboid: length 2a, width 2b, height 2c, circumscribed ball radius R=(a +b +c) square.

Triangular cone: triangular cone ABCD, with triangle ABC as the base and D as the vertex (all four points of ABCD are in the coordinate table.

Show).

First, find out the center o of ABC's circumscribed circle (that is, the intersection of the perpendicular lines of any two sides);

Second, make ABC's vertical line through point O;

3. Let a point E on the vertical line make ED=EA (or ED=EB or ED=EC) form an equation.

Find the coordinates of point e;

The radius of the outer sphere R=EA=EB=EC=ED.

Multiple (four or more) pyramids: The polygon at the bottom must be a regular polygon (the quadrilateral can be a square or a rectangle).

Shape),

First, find out the center o of the circumscribed circle of the polygon on the bottom (that is, the intersection of the perpendicular lines of any two sides). If you find it,

If there is no circumscribed circle center, then the polygon pyramid has no circumscribed ball;

Second, the intersection o is the vertical line of the bottom surface;

Third, set a point E on the vertical line so that ED=EA (or ED=EB, or ED=EC ...) can be listed aside.

Cheng, find the coordinates of point e;

The radius of the outer sphere R=EA=EB=EC=ED= .....

Prism: 1. Find out the circumscribed centers of the two bottom surfaces of the prism;

2. Connect the centers of the circumscribed circles of the two bottom surfaces, and find the midpoint m of the connecting line;

3. The connecting line between the point m and any vertex of the prism is the radius r of the circumscribed sphere.

I don't know if I can understand it without drawing. You can leave a message if you need to communicate.