## Friday, April 2, 2010

### Matzo Balls Puzzle

Who doesn't love chicken soup? How about a special but rare treat of chicken soup with Matzo balls? During the recent Passover celebration my kids were helping me to roll these balls from the Manischewitz Ball Mix. According to the package directions, it was enough to make around 10 balls of diameter 1". We had two packs and I realized that it is not going to be enough as kids wanted to have more than two for everyone. We decided to make the Matzo balls smaller, with 0.5" diameter. Can you help me to estimate how many balls we will end up having?

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Kim said...

The volume of a sphere is 4/3*pi*r^3

A 1" diameter ball has a .5 radius or a volume of 4/3 * pi * .125

a .5 diameter ball has a .25 radius or a volume of 4/3 * pi * .015625, which is 1/8 the volume of the 1" ball.

So if you can make 10 1" balls, you can make 80 1/2" balls.

Kim said...

80.

Since the volume of a sphere is a function of r^3 and (1/2)^3 = 8*(1/4)^3, you can make 8 times as many matzo balls with a 1/2" diameter as with a 1" diameter.

Kim said...

Wait, one thing... if it was 10 balls/pack and you have two packs, then you'd actually end up with 160. But if you meant that the two packs had enough make 10, then I'll stick with my 80.

Anonymous said...

Estimate 8 times as many dumplings, if you cut the diameter (or the radius) in half.

4/3 pi r cubed.

80

tom

Maria said...
This comment has been removed by the author.
Maria said...

Commenting has not been working smoothly today. However both master solvers above managed to submit their solutions. Never hesitate to just email the solution to me if blogger interface doesn't work. The time of your email is considered to be the official "solution time."

Kim was first and gets her ... 34th puzzle point!

Maria said...

test

Kim said...

By the way, I'm betting 80 matzoh balls is more than you needed, so please feel free to send some over our way! Our family's seder had to be cancelled because of flooding, and we could use some matzoh ball soup here!!

Maria said...

So sorry to hear about flooding. Some of my neighbors also got it. We would have invited you if we knew earlier. I saw the great picture your kid made of you on Facebook (Kim as a mommy-devil). It seems that your kid(s) will manage very well with my kids.

Kim said...

LOL!