The Paratha Puzzle

The story

This story took place in Riya’s kitchen last Sunday. Aai made two parathas: one was tiny and thick, while the other was huge but thin. Riya immediately guessed that the bigger paratha had more dough, because it looked larger and she thought size meant more food. But things changed when Aai cut into both parathas, the thick one felt heavier. When Riya weighed them, the small paratha was actually heavier than the big one. Was it paratha magic or extra atta? Aaji reminded everyone to think mathematically: it's the volume that matters, not just the area. Suddenly, Riya realised her mistake. Now, whenever she picks a paratha, she checks its thickness first. Which would you pick: huge and thin, or thick and tiny?

The science

The amount of dough in a paratha depends on its volume, not just its surface area. Surface area of a circle is calculated using pi r squared as taught in Class 10 Mathematics, but this only shows the area on top. The amount of dough is determined by multiplying that area by the thickness of the paratha, which gives the volume. This means a small but thick paratha might have more volume, and therefore more dough, than a large but thin one. The textbook term for this is ‘volume of a cylinder’, in this case, the paratha.

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Questions students ask