I don’t know what all that Rose factor stuff is because I don’t have that particular book and her quirky methods aren’t taught in culinary schools.

But I do have a heavenly cakes. I’ve been taught how to scale by national culinary standards. To convert the recipe from a single 9 inch round to a single 12 inch round you first need to find the area difference between the two round pans. But doing the calculations, you will see that the 12” round quantity is too much for a 10” square. Makes better sense to scale the the 10” square.

So here’s all the math. At the bottom I include the recipe scaled to a 10” square.

The area is the radius squared multiplied by pi.

The radius is half the diameter

Pi = 3.14

9” is the diameter So divide it in half for radius

9 divided by 2 = 4.5 Now square the radius

4.5 x 4.5 = 20.25 Now multiple by pi

20.25 x 3.14 = 63.65

Area of 9” is 63.65”

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12” is the diameter So divide it in half for radius

12 divided by 2 = 6 Now square the radius

6 x 6 = 36 Now multiple by pi

36 x 3.14 = 113.04

Area of 12” is 113.04

Divide larger pan area by smaller pan area

113 divided by 64 = 1.765

Look at the number to the RIGHT of the decimal point. That tells the the percent to increase the batter. The 12” pan requires 76% more batter.

So you need 1 full recipe PLUS 76%

STOP! you state that you want bake a 10 inch square cake. But you intent to use a 12” round pan as the basis for the conversion. You will end up with about 20% more batter than you need.

To find the area of a square you simply multiple the length by width.

10 x 10 = 100.

The area of a 10” square is 100”

Divide the larger size pan into the smaller size 9” pan from the recipe

100 divided by 64 = 1.56

The 12” round requires .76 more batter

The 10” square requires .56 more batter

20% is a significant difference.

So it makes more sense to scale the recipe to the 10” square and not the 12” round.

Since .56 is close to 60, for ease of calculations, you can use .60.

Unsweetened alkalized cocoa powder 42 g

42 x .60 = 25.2 You need an additional 25.2 grams cocoa powder

42 + 25.2 = 67.2 cocoa powder

Boiling water 118 grams

118 x .60 = 70.8 You need a additional 70.8 grams boiling water

118 + 70.8 = 188.8 gram boiling water

Whole eggs 100 grams

100 x .60 = 60 You need an additional 60 grams of whole eggs

100 + 60 = 160 grams of whole eggs

Water 44 grams

44 x .60 = 26.4 You need an additional 26.4 grams water

44 + 26.4 = 70.4 grams water

Cake flour 156 grams

156 x .60 = 93.6 You need an additional 93.6 grams cake flour

156 + 93.6 = 249.6 grams cake flour

Sugar 200 grams

200 x .60 = 120 grams You need an additional 120 grams sugar

200 + 120 = 320 grams sugar

Baking powder 2 teaspoons OR 10 grams

2 x .60 = 1.2 You need 1.2 additional teaspoons baking powder

2 + 1.2 = 3.2 teaspoons baking powder

OR

10 x .60 = 6 You need 6 grams more baking powder

10 + 6 = 16 grams of baking powder

Salt 1/2 (same as .5) teaspoon OR 3 grams

.5 x .60 = .3 You need an additional .3 of a teaspoon

.5 + .3 = .8 of a teaspoon of salt

OR

3 x .60 = 1.8 grams You need 1.8 grams additional salt

3 + 1.8 = 4.8 grams salt

Butter 113 grams

113 x .60 = 67.8 You need an additional 67.8 grams butter

113 + 67.8 = 180.8 grams butter

Oil 28 grams

28 x .60 = 16.8 You need an additional 16.8 grams oil

28 + 16.8 = 44.8 grams oil