What does Armand want and why

either a donut or a sphere or a pancake or a flat sphere. it depends on where the vertical line is.

if the line goes through the center of the circle and is perpendicular to a diameter containing the center, then you get a flat circle.

if the line and the diameter of a the circle meet in the center of the diameter and at an angle, you get a pancake.

if the line is on the circumference of the circle and is at right angles   to the circle you get a ring.

if the line contains the diameter, you get a sphere.

the the line is parallel to the diameter and touches the circumference, you get a donut.