Given a right circular cone, you put an upside-down cone inside it so that its vertex is at the
center of the base of the larger cone, and its base is parallel to the base of the larger cone. If
you choose the upside-down cone to have the largest possible volume, what fraction of the
volume of the larger cone does it occupy? (Let H and R be the height and radius of the large
cone, let h and r be the height and radius of the small cone. Use similar triangles to get an
equation relating h and r.) Can someone help me get started on this? I have a picture drawn. What are the equations I need?

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