Calculating volume of a cake recipe

[jgarner53]

Can someone help me out here? I have a cake recipe that a neighbor wants me to make for him. The recipe makes three 9-inch layers (I am going to assume because this was published in "Southern Living" magazine that we're talking about 1 1/2-inch deep cake pans because that's what your average home baker has on hand.)

He has told me that he doesn't need a whole 9-inch cake, so I was thinking I'd make an 8-inch cake and bake the rest into a small 6-inch cake. But I'm trying to figure out how much batter the recipe makes, so I can figure out if I should do three 8-inch layers, or just two (and tort them), to have enough batter leftover for the 6-inch cake.

In the recipe, the butter is melted, and the eggs are just beaten, so we don't have to calculate the added volume of air from creaming or whipping eggs or egg whites. Here are the quantities:

1 1/2 c. butter

3/4 c. water

4 oz. white chocolate (melted)

1 1/2 c. buttermilk

4 large eggs, lightly beaten

1 1/2 tsp. vanilla extract

3 1/2 C. all-purpose flour (here we will have to guess on an ounce-weight, since it is not given)

1 c. chopped pecans

2 1/4 c. sugar

1 1/2 tsp. baking soda

Now I know I should have paid more attention in algebra! Or was that geometry?

For the record, I found online that a 9 x 1-1/2 inch cake pan holds 6 cups, and an 8 x 1-1/2 inch cake pan holds 4 cups.

help!

[culinary bear]

Eeep.

Right, assuming the cake tins are all 1.5 inches deep, the only varying factor is the diameter, in this case 9, 8, and 6 inches.

As the volume of any cylinder (essentially a standard round cake) depends on the sqaure of the radius, that gives the following :

volume of a 9 inch diameter cake = 9/2 x 9/2 = 81/4 = 20.25 units

8 inch = 64/4 = 16 units

6 inch = 36/4 = 9 units.

If your original recipe made enough for 3x9 inch layers, that gives a hypothetical volume of batter of 60.75 units.

3x8 inch layers would need 48 units, adding your 6 inch cake would take you to 57 units, and you'd still have enough left over to give you a good go at licking the bowl afterwards.

[jgarner53]

I'm not sure I follow your math (really, I glaze over so quickly on this kind of thing), but I'll take your word for it. Of course, the proof will be in the pud-er- cake, I guess. Thanks!

[Patrick S]

As CB pointed out, cake pans are cylinders, so you can calculate their volumes by the formular pi x r^2 x h, where r and h are radius and height, in this case in inches.

So, the volume of a 9" diameter, 1.5" high pan is: 3.14 x 20.25 x 1.5= 95.3775 square inches, the the volume of an 8" pan is 3.14 x 16 x 1.5= 75.36 square inches, and that of a 6" is 3.14 x 9 x 1.5 = 42.39.

Three 9" pans are about 285 sq in in volume. Three 8" pans are 225 in sq. So, assuming you're filling all the pans to the same depth, I think you'd have enough batter left over to fill roughly one and a half 6" pans.

The real question is, if train A and train B are on a straight track 100 miles apart, and train A is moving north at 60 miles an hour, and train B is moving south at 80 miles an hour, and train A is decelerating at a rate of 10 miles per hour per hour, at what point will your head explode?

Seriously though. Check my math before you bake anything. . .

[JSkilling]

I find it easier to take this one step further and get it in fluid ounces so I can work from there. I glazed over as well, but in the end this is not hard math:

9" Pan - Formula

Pi (3.14159) * (radius * radius) = square inches

Square inches * height = cubic inches

Cubic inches * fluid ounces per cubic inch (0.5542113) = fluid ounces

That's how they figured the 9" pan holds ~6 cups. But I don't think this yet solves your problem because you still only know that your recipe will yield enough batter for 3 9" layers. It doesn't say how much to fill, how much rise you'll get, etc. And you don't fill the pans all the way to the top - probably half or 2/3 full.

So here's the easy way I'd have done this:

9" pans at 6 cups each (but you'll fill halfway so 3 cups)

3 cups * 3 layers = 9 cups of batter you expect to yield for this recipe

8" pans at 4 cups each (but you'll fill halfway so 2 cups)

2 cups * 3 layers = 6 cups of batter required for the 3 8" layers

You have 3 cups of batter left, enough for a 9" layer or one 6" and some cupcakes.

When in doubt I just go the the kitchen and fill the measuring cup Patrick's math got you to the same place but I think it's harder to understand the square inches. If we can get this into units of measure we understand I think it's easier to grasp. After all, the president of Harvard said we poor women folk can't do math

[chefpeon]

Pi (3.14159) * (radius * radius) = square inches

Square inches * height = cubic inches

Cubic inches * fluid ounces per cubic inch (0.5542113) = fluid ounces

Gosh, I love all you pi people! Sigh.....the only pi I know much about is apple.....pumpkin....cherry......banana cream.......

Seriously, though, math is not my greatest subject either. I'm competent.....but still.....if I can avoid *math* I will!

This is what I'd do: (really)

1. Make the batter.

2. Pour into pans.

3. If I have some left over, I bake mini bundts, or cupcakes, or a 6 incher or whatever.

4. If I don't, well.....great!

5. If I need more, I make another batch.

Oh.....sure.....you may LAUGH at my simpleton ways!

But you know, I've always found it extremely handy to have extra cakes hanging around in my freezer when some bonehead calls to make that last minute order 'cause they FORGOT Mom's birthday was tomorrow. My simpleton ways just saved that guy's ass....so.......everyone wins!

And I don't have to do math!

YAY!!!!!!!

[Behemoth]

I'm okay with the math, but what do you do about baking times?

[Tepee]

This is what I'd do: (really)

1. Make the batter.

2. Pour into pans.

3. If I have some left over, I bake mini bundts, or cupcakes, or a 6 incher or whatever.

4. If I don't, well.....great!

5. If I need more, I make another batch.

←

Hey, I do that too!

I also write down for future reference beside the recipe the size of pan I used and the bake time.

[JSkilling]

Ok, now that I just spit all over my screen from laughing.....

I was forced into this math to order some dessert rings. The scary part is I can do it, make it work and so totally understand it. And I am so not a math girl!

My methods are actually quite similar to Anne's, though I'd have to insert cussing in there somewhere because *&%*^)$)) I don't have enough to fill this pan and need to get it baked in the next 15 minutes!!!!! Then I scream why didn't I just take the time to measure this so I'd know and wouldn't be short. AAAAGGHHHHHHH.....

[chefpeon]

I'm okay with the math, but what do you do about baking times?

Well, gosh, that's the easy part. The smallest cakes will be done first. If the recipe states "30 minutes in a 350 degree oven" for a 9 inch cake, then I can safely assume that if I bake a 6 inch cake or little bundt cakes, these are going to take significantly less time. So I cut the time in half and set the timer for 15 minutes. At 15, I check their progress.....if they're done,

I pull them, and if not, I make a guesstimate depending on degree of doneness about how much more time the cake (or cakes) need. Then keep checking.

[rjwong]

This topic seemed familiar to me and it was:

http://forums.egullet.org/index.php?showtopic=61027

jgarner53, in this discussion thread about Scaling from an 8 inch to a 9 inch pan, there are a couple of excellent links to websites that have done the math already.

http://www.baking911.com/pantry_substitutes_pansizes.htm

www.pastryscoop.com

Just bookmark these and bake!

[Behemoth]

At 15, I check their progress.....if they're done,

I pull them, and if not, I make a guesstimate depending on degree of doneness about how much more time the cake (or cakes) need.

See, to me the math is easy. It's the guesstimating that's the hard part

Well, OK some math is not so easy...

[jgarner53]

This topic seemed familiar to me and it was:

http://forums.egullet.org/index.php?showtopic=61027

jgarner53, in this discussion thread about Scaling from an 8 inch to a 9 inch pan, there are a couple of excellent links to websites that have done the math already.

http://www.baking911.com/pantry_substitutes_pansizes.htm

www.pastryscoop.com

Just bookmark these and bake!

For all my googling this topic yesterday, why couldn't I find it? Thanks! It's going in my bookmarks now.

[melmck]

I'm with chefpeon, make plenty of batter, save extra for minis, cupcakes whatever, or just put it in a container and thaw later. keep an eye on your oven to figure out baking times! check at 15 minutes and every 5-7 minutes after that.

[rooftop1000]

You could get an aproximate formula for baking times off the back of a boxed cake mix..... I think they put all sorts of pan choices on there ....not that I look or anything....

T

[jgarner53]

Result: 8 cups batter total: 2 for each cake layer, plus 10 1/2-cup cupcakes.

Bake time: 23 minutes for the cake layers, cupcakes are currently in the oven, but I'm thinking 15-20.