2.06.2008

how nerds make dessert, part two

for the original how nerds make dessert, click on it.

by way of introduction, a vignette
Cassie: OK, baking opinion sought. if a recipe fills a 9x9 pan, do you think doubling it would be enough to make a pan of cupcakes?
me: this is a MATH question!
Cassie: i was just figuring that a pan of cupcakes is maybe half again as wide as a 9x9 pan. and they each require more depth. so maybe it would come out evenish.

Since I am at work and have only Google at my disposal, this experiment is being conducted entirely in the realm of theory and internet searches.

A 9x9 pan filled to one even inch holds 81 cubic inches of batter.
A standard cupcake pan holds twelve cupcakes, with each cup 2.75" wide and 1.25" deep, which means each cupcake cup holds 7.42446701 cubic inches of batter.

BUT that's me assuming a cupcake cup is a perfect cylinder. It's not! It's cone with the bottom cut off.* But I am going to deal with that by arbitrarily rounding down our 7.42etc to 7.25, and just make it an even 7 because no one ever really fills a cupcake pan to the top if they know what's good for them.

81 divided by 7 is about 11.6, which is almost the 12 cupcakes it takes to fill a pan. And if your cake recipe is the type to fill a 9x9 pan to 1.5 inches rather than 1, you're looking at 121.5 cubic inches of batter, which is seventeen cupcakes, plus a little leftover batter for spoon-licking.

But then there is also the critical matter of frosting.

The surface area of a 9x9 cake is an easy 81 square inches, but the surface area of a cupcake of width 2.75" (even though we didn't fill the cupcake cups to the top, they puff up when they're cooking) is about 5.9 square inches, which let's round up to an even six due to its domed shape, which times 12 is only about 66 square inches - 80% of the amount needed for a 9x9 cake. Though if you're going the seventeen-cupcake route, you need 102 square inches of frosting, which is about one-and-a-half times the amount needed for an even dozen (which, duh, makes sense, since 17 is about one-and-a-half times twelve), or 125% of the 9x9 quantity.

All of which is to say, in summary: No, Cassie, you do not need to double your recipe. But you can if you want to, and make extra cupcakes, and give them to me.



*another vignette:
me: hey, what is the name for a shape that is a cone with the point cut off?
me: like a dixie cup or a cupcake
my brother: circumcision?

5 comments:

Marcin said...

story I have to compete is the time Kit and I were making Barefoot Contessa brownies, using a round tin. Kit asked if the 9 inch round tin was too big (given that the recipe called for a 7 inch square tin), and running around the house I found a working computer and got google to compute the answer.

The answer is that they are the same size. If this seems much simpler, it is because we make more efficient life choices.

A is A said...

J'adore Barefoot Contessa brownies! Further, the thought of round pan brownies truly excites me because you could cut the brownies like pie and you could have...BROWNIE PIE! Holy mother.

Please ignore the notion that in order to be considered pie one must have crust + filling...desserts are open to artistic interpretation.

Marcin said...

Listen, I'm willing to defend pie to the death. I reckon that a brownie mix might be used as a thin-layer crust around unsugared compoted apricots.

A is A said...

Touche good sir! I must respect anyone who will fight in the name of pastries.

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