A family plans to share a hemispherical cake.  The cake has a diameter
of
nine inches, and is covered (except on the flat side) with a one- half
inch thick layer of frosting, so that the resulting cake has a diameter
of
ten inches.

It's cut into five two-inch thick pieces by making parallel vertical
slices perpendicular to the bottom of the cake.  Mom and Dad take the
first two pieces (counting from one end) and the children (Alex,
Barbara,
and Charlie) take the next three.  (Alex has the slice from the middle
of
the cake and Charlie has the end slice.)  Obviously Alex gets the most
cake, but the children want to know who gets the most frosting? 

[There's a picture on the paper copies of the problem available from the
bulletin board display in the Chauvenet lab deck corridor.]

There will be a $1 prize for the best correct solution submitted by a
midshipman.

A solution is "correct" if it answers the question correctly and
explains
the answer; a solution is "best" if it includes the clearest correct
explanation.  Solutions are due by noon on Thursday, April 15, 1999.
Submit solutions to Prof. Hanna at mathprob@nadn.navy.mil, or via the
mailbox in Chauvenet 301.




Correct solutions to problem #92 (the circles inscribed in the triangle)
came from Midn 1/c Wood,
Midn 2/c Frommel, Kim, and Terry (I think), Midn 3/c Feist and Hodges,
and
Midn 4/c Stepp and
Whitten.  The radius of the smaller circle is the square root of 3
divided
by 18.  Midn Wood's
prize-winning solution is posted on the bulletin board in the Chauvenet
lab deck corridor.