Math problem: Recipe for cake calls for TWO 9" pans filled with batter. What size pan should I use if I just want one pan of cake?

Trying to keep the amount of ingredients intact. This recipe is from Babbo's Pan di Spagna web site.

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ChrisBird
ChrisBird January 15, 2012

It cooks very differently if you change the pan size. The new pan size you need assuming the same depth is 12 3/4 . But I don't think it will come out well

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GIOVANNI50
GIOVANNI50 January 15, 2012

How did you arrive at this number?

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SarahSoda
SarahSoda January 15, 2012

If your 2 pans are 9 X 2, then they each hold from 3 to 31/2 cups of batter. If you want to substitute an oblong pan, that amount of batter would fit in a 9 X 13 pan based on the amount of batter. You may have to adjust the cooking time, so keep an eye on how it raises.

This is from a "Piece of Cake" by Susan Purdy.

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creamtea
creamtea January 15, 2012

I use this cookbook all the time!

ChrisBird
ChrisBird January 15, 2012

Straightforward math! 1 pan has area pi x 4.5 x 4.5 = pi x 20.25. 2 pans have area pi X 40.5. So to get the same area, the radius of the new pan must be about the square root of 40.5. That is around 6.375. So the diameter must be twice that. That's the first principles way.

The way I actually did it was to multiply 9 by the square root of 2 (1.414...) and round it off.

As SarahSoda said, if you change the shape of the pan you will have to watch carefully. The mixture will be slight;y deeper in the 9x13 pan.

I hope this was a cooking question not a homework question!

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GIOVANNI50
GIOVANNI50 January 15, 2012

ChrisBird Thanks. Your calculation holds the height constant. You are holding the area constant but it is really the amount of batter that is constant, i.e., the volume. So there is another SQRT of the ratio of the two heights of batter. We'll presume it is the same and try. No it's not a HW problem... I wish...

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ChrisBird
ChrisBird January 15, 2012

lol, I was assuming that I held the height constant because that gives a shot at getting the rise to work. If you hold the height constant, it cancels out of the equation, so it really doesn't matter. You will have the same height in each pan with the same amount of batter. I just left that out. so to show the math properly (assuming height h in the 2 pan version).
Volume of batter = 2 x pi x h x 4.5x 4.5 = pi x h x 2 x 4.5 x 4.5
That equals pi x h x 2 x 20.25 = pi x h x 40.5
To get that into a single pan (to height h) that means the pan must be sqrt (2 x 4.5 x 4.5) in diameter. Note that the pi and the h are constant

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ChrisBird
ChrisBird January 16, 2012

ooops that last line should have read sqrt (2 x 4.5 x 4.5) in RADIUS, not diameter. Apologies all.

nutcakes
nutcakes January 15, 2012

She gives a 17-inch jelly roll as an alternative pan (though I don't know why the pic is a loaf)
http://www.babbonyc.com/dolci-pandispagna.html

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