Additional Mathematics Project
Question Part I Cakes come in a variety of forms and flavours and are amongfavourite desserts served during special occasions such asbirthday parties, Hari Raya, weddings and etc. Cakes aretreasured not only because of their wonderful taste but also inthe art of cake baking and cake decorating. Find out howmathematics is used in cake baking and cake decorating andwrite about your findings. Answer: Geometry ± To determine suitable dimensions for the cake, to assist in designing and decorating cakes that comes in many attractive shapes and designs, to estimate volume of cake to be produced Calculus (differentiation) ± To determine minimum or maximum amount of ingredients for cake-baking, to estimate min. or max.amount of cream needed for decorating, to estimate min. or max. size of cake produced.
Progressions ± 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 cream for decoration.
Part II Best Bakery shop received an order from your school to bake a 5 kg of round cake as shownin Diagram 1 for the Teachers¶ Daycelebration. (Diagram 11)
1)
If a kilogram of cake has a volume of 3800 , and the height of the cake is to be 7.0cm, calculate the diameter of the baking tray to be used to fit the 5 kg cake ordered by your school. = 3.142]
[Use
Answer: Volume of 5kg cake = Base area of cake x Height of cake 3800 x 5 = (3.142)( )² x 7 (3.142) = ( )² 863.872 = ( )² = 29.392 d = 58.784 cm 2)The cake will be baked in an oven with inner dimensions of 80.0 cm in length, 60.0 cmin width and 45.0 cm in height. a)If the volume of cake remains the same, explore by using different values of heights,hcm, and the corresponding values of diameters of the baking tray to beused,d cm. Tabulate your answers
Answer: First, form the formulafor d in terms of h by using the above formula for volume of cake, V = 19000, that is: 19000 = (3.142)(d/2)²h
=
Progressions ± 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 cream for decoration.
Part II Best Bakery shop received an order from your school to bake a 5 kg of round cake as shownin Diagram 1 for the Teachers¶ Daycelebration. (Diagram 11)
1)
If a kilogram of cake has a volume of 3800 , and the height of the cake is to be 7.0cm, calculate the diameter of the baking tray to be used to fit the 5 kg cake ordered by your school. = 3.142]
[Use
Answer: Volume of 5kg cake = Base area of cake x Height of cake 3800 x 5 = (3.142)( )² x 7 (3.142) = ( )² 863.872 = ( )² = 29.392 d = 58.784 cm 2)The cake will be baked in an oven with inner dimensions of 80.0 cm in length, 60.0 cmin width and 45.0 cm in height. a)If the volume of cake remains the same, explore by using different values of heights,hcm, and the corresponding values of diameters of the baking tray to beused,d cm. Tabulate your answers
Answer: First, form the formulafor d in terms of h by using the above formula for volume of cake, V = 19000, that is: 19000 = (3.142)(d/2)²h
=