Step 1, change 10 inch to 12 inch. As follows:

Calculation principle:

Calculating the amount of materials needed by molds with different sizes is actually calculating the volume gap of cakes made by molds with different sizes.

The calculation formula of cylinder volume is: bottom area × height. In actual production, although the size is different, the height of the cake is the same, so the proportion of volume is actually the proportion of the bottom area.

The formula of the bottom area is π× the square of radius, which is actually the ratio of the square of radius.

For example, an 8-inch cake mold: 10-inch cake mold =8/2 square: 10/2 square =16: 25 =1:1.56.

According to the table, 10 inch cake is converted into 12 inch cake = 1: 1.44.

The data in the table are accurate calculation values. In fact, when we convert, we can take a relatively easy approximation. For example, we usually encounter the most, and the amount of 8 inches is converted into 6 inches. According to the values in the table, all the ingredients should be multiplied by 0.56, but for the convenience of calculation, we usually halve the ingredients directly, that is, multiply them by 0.5.

The second step is to transform the circle into a heart.

The calculation of the heart-shaped area is complicated, involving the coordinates and symmetry axis of the heart-shaped line set, and the formula is

The cardioid ρ = a (1+cos θ) (a > 0)

dA= 1/2*ρ^2dθ？ = 1/2*a^2？ ( 1+cosθ)^2dθ

Because the image is axisymmetric, we just need to find the area of 1/2 and then double it, where the upper limit of π is 0.

Of course, the upper limit of 2π can be selected.

Lower bound π

So the bottom area of different molds is different, but you can probably think that the heart shape is about 70% of the circle of the same size (it may be estimated to be a little too much, so it is best not to lose too much).

Install 70% of 10 inch cake, which is converted into 12 inch heart-shaped cake =1:(1.44x70%) =1:1.008.

That is to say, the formula for converting 10 inch cake into 12 inch heart-shaped cake is basically one to one.

Oh, my God! ! It is too complicated. It seems that if you want to learn baking, you have to learn math first! ! !

I hope it helps you.

I thought of a simple way, provided that 10 inch cake mold and 12 inch cake mold are not detachable bottoms.

1, you can mold 10 inch cake until it is full of water, pour the water in the mold on the scale and weigh it to get one.

2. Add 12 inch center & #10084; Mold the cake until it is full of water, pour the water in the mold on the scale and weigh it to get B.

3, 10 inch cake is converted into 12 inch heart-shaped cake = A: B (I estimate that the ratio will probably not exceed 1: 1. 1, depending on the radian of the upper and lower limits of the heart, so it is close to1:/kloc-0.

Remember this ratio. . . . . . good

In addition, if it is a movable bottom die, it can also be solved If you weigh it with flour, will you still lack flour when making cakes? Do it quickly, don't wait, O(∩_∩)O hahaha ~ (the answer has been revised n times)