MATHEMATICS IN CAKE BAKING AND CAKE DECORATING

GEOMETRYTo determine suitable dimensions for the cake, to assist in designing and decoratingcakes that comes in many attractive shapes and designs, to estimate volume of cake to be produced When making a batch of cake batter, you end up with a certain volume, determined by the recipe. The baker must then choose the appropriate size and shape of pan to achieve the desired result. If the pan is too big, the cake becomes too short. If the pan is too small, the cake becomes too tall.This leads into the next situation.

 The ratio of the surface area to the volume determines how much crust a baked good will have.The more surface area there is, compared to the volume, the faster the item will bake, and theless "inside" there will be. For a very large, thick item, it will take a long time for the heat to penetrate to the center. To avoid having a rock-hard outside in this case, the baker will have tolower the temperature a little bit and bake for a longer time.We mix ingredients in round bowls because cubes would have corners where unmixedingredients would accumulate, and we would have a hard time scraping them into the batter.

CALCULUS (DIFFERENTIATION)

To determine minimum or maximum amount of ingredients for cake-baking, toestimate min. or max. amount of cream needed for decorating, to estimate min. or max.Size of cake produced.

PROGRESSION

To determine total weight/volume of multi-storey cakes with proportional dimensions,to estimate total ingredients needed for cake-baking, to estimate total amount of creamfor decoration.For example when we make a cake with many layers, we must fix the difference of diameter of the two layers. So we can say that it used arithmetic progression. When the diameter of the firstlayer of the cake is 8´ and the diameter of second layer of the cake is 6´, then the diameter of thethird layer should be 4´.In this case, we use arithmetic progression where the difference of the diameter is constant that is2. When the diameter decreases, the weight also decreases. That is the way how the cake is balance to prevent it from smooch. We can also use ratio, because when we prepare the ingredient for each layer of the cake, we need to decrease its ratio from lower layer to upper layer. When we cut the cake,

we can use fraction to devide the cake according to the total peoplethat will eat the cake.

Best Bakery shop received an order from your school to bake a 5 kg of round cake as shown in Diagram 1 for the Teachers¶ Day celebration.

If a kilogram of cake has a volume of 38000cm3, and the height of the cake is to be 7.0 cm, the diameter of the baking tray to be used to fit the 5 kg cake ordered by your school 3800 is Volume of 5kg cake = Base area of cake x Height of cake

3800 x 593.142 = (3.142)(d/2)219000/7(3.142) = (d/2)2

863.872 = (d/2)2

d/2 = 29.392d = 58.784 cm

2) The cake will be baked in an oven with inner dimensions of 80.0 cm in length, 60.0cmin width and 45.0 cm in height.

a) If the volume of cake remains the same, explore by using different values of heights, h cm, and the corresponding values of diameters of the baking trays to be used, d cm. Tabulate your answers.

b) based on the values in your table,

(i) state the range of heights that is NOT suitable for the cakeand explain your answers.