Free Republic
Browse · Search
News/Activism
Topics · Post Article

To: bcoffey
If a pie pan is 9" across, and you remove a piece of pie 3" across at it's widest, how many pieces of pie are left?
60 posted on 09/16/2002 8:50:35 AM PDT by FreedomFarmer
[ Post Reply | Private Reply | To 58 | View Replies ]


To: FreedomFarmer
If a pie pan is 9" across, and you remove a piece of pie 3" across at it's widest, how many pieces of pie are left?

Oh, boy!!!! A word problem!

Let's see. If the pan is 9" across, then its radius, and each cut side of a piece, is 4.5".

The widest part of the cut piece is 3", which is a chord of the pie circle.

Consider the cut piece to be composed of two right triangles, back to back, with their adjoining right angles at the center of the chord.

Then, each triangle has one side (the hypoteneuse) of 4.5" and the side opposite the central angle of 1.5".

The sine of this ratio, 1.5/4.5 or 1/3, is approximately 19.47 degrees.

Since the slice is made up of two such triangles, its included angle is 38.94 degrees.

Therefore, the entire pie would consist of 360/38.94 slices of this size, or about 9.244 slices.

Now, if you remove one slice of this size from the whole pie, the number of pieces which remain is,

ummmm,

one.

93 posted on 09/16/2002 4:00:47 PM PDT by Erasmus
[ Post Reply | Private Reply | To 60 | View Replies ]

Free Republic
Browse · Search
News/Activism
Topics · Post Article


FreeRepublic, LLC, PO BOX 9771, FRESNO, CA 93794
FreeRepublic.com is powered by software copyright 2000-2008 John Robinson