Saturday, May 2, 2009

Marshmallow smooshing

This is a puzzle dedicated to my dear brother who is celebrating his birthday today.

Back in our childhood, we always impatiently anticipated and throughfully enjoyed after-dinner desserts. Candies, marmalades, marshmallows. Except that my little brother used to have peculiar dessert eating habits. He always smooshed the marshmallows, by pressing them down to the table with his palm. My parents mused that, looking from the top, a smooshed marshmallow does look bigger than intact, and so he is probably thinking that he found a way of making more from less.

Here is the puzzle:
Marshmallow is a cylinder of height 1" and diameter 1". If you smoosh it so that its diameter becomes 2", what would be it's height? Assume that the volume stays the same. Most of us (including me), obviously, do not remember how to compute the volume of a cylinder. But nowadays this is easy to find in the internet. You can also try it empirically, with a real marshmallow. However, your answer would be counted only if you provide thorough and convincing explanation.


rachel_t said...

Volume of cylinder is Area of circular cross section x height

A1 x h1 = V1
A2 x h2 = V2
V1 = V2
so A1 x h1 = A2 x h2
or A1/A2 = h2/h1

A = pi x D/2 x D/2

A1/A2 = pi x D1/2 x D1/2 = D1 x D1
---------------- -------
pi x D2/2 x D2/2 D2 x D2

substitute D2 = 2 x D1
A1/A2 = D1 x D1 1
--------------- = -
2 x D1 x 2 x D1 4

h2/h1 = 1/4
so h2 = h1 x (1/4)

h1 = 1, so h2 = 1/4 or 0.25"

rachel_t said...

oops, I should have previewed, it's difficult to decipher the fractions I tried to show.

Maria said...

Wow, someone has been solving puzzles in the middle of the night.... You see, Celtics game just does not give enough of adrenaline rush. Rachel T takes a two point lead over Amy, with the rest tailing behind.

The answer is correct. And it is actually simpler than it looks.
volume of a cylinder = Pi * R^2 x H
we have first time R=0.5" H=1"
smooshed mashmallow: R=1" H=?

0.5^2 x 1 = 1^2 x H
0.25 = H

so, smooshed marshmallow cylinder will have a height of 0.25"

Laura Grill said...

.25" because you take the volume of both and put them on both sides of the equation because the volume stays constant. Then you solve for x which is the height of the smooshed marshmallow.

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