Math Is Fun Forum

MoyMarian

Member

Registered: 2009-01-10

Posts: 29

Solid Mensuration XIV

A plastic container is in the form of a right circular cylinder with a large conical opening. When it is filled level with the bottom of the opening, it can just be turned upside down without spilling the content. Prove that the depth of the cone is three-fifths the depth of the container.

Last edited by MoyMarian (2009-01-15 17:16:05)

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Solid Mensuration XIV

Let

be the depth of the cone

be the depth of the cylinder

be the cross-sectional area

The volume of the cone is

. Thus the volume of the water in the upside-down cone is

.