An ink bottle is in the form of a right circular cylinder with a large conical opening as shown in the figure. When it is filled level with the bottom of the opening, it can just be turned upside down without any ink spilling. Prove that the depth of the cone is 3/5 the depth of the bottle.

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Cylinders

A cylinder is a three-dimensional solid shape with two parallel and congruent circular bases, joined by a curved surface at a fixed distance. A cylinder has an infinite curvilinear surface.

Cones

A cone is a three-dimensional solid shape having a flat base and a pointed edge at the top. The flat base of the cone tapers smoothly to form the pointed edge known as the apex. The flat base of the cone can either be circular or elliptical. A cone is drawn by joining the apex to all points on the base, using segments, lines, or half-lines, provided that the apex and the base both are in different planes.