Five Equal Pieces of a Square Cake
Date: 05/22/2001 at 05:38:00 From: Katie Subject: Maths challenge problem Ravina has a square birthday cake. Its side length is 20cm. She wishes to cut the cake into five pieces, one for each of her four friends and one for herself. She wants to use straight vertical cuts to make five pieces of equal volume. Suppose that Ravina makes the first cut from the cake's center to a point from the top left corner. Where must she make the other four cuts if they all start for the cake's center? I haven't even started... I would not even know where to start. Please help me!
Date: 05/22/2001 at 12:24:52 From: Doctor Peterson Subject: Re: Maths challenge problem Hi, Katie. A good place to start is to think about what the area will be for any wedge cut from the cake, like this: +-----------+ | | | | | + | | / \ | | / \ | +--------+--+ |<---d-->| Once you've done that, think about the area of a wedge that goes around a corner, like this: +-----------+ | | | | | +__ | | / \ | | / --+ -- +-----------+ ^ |<-------d-----+ You will find that the distance d along the outside is all you need to know, and using that you can find the correct value of d for which each piece is 1/5 of the cake. The answer is surprisingly simple! - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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