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    Nur Shahirah Bt Mohd Nazri

    5 Bestari

    940427-07-5168

    PA030A129

    SMK Convent Green Lane

    Pn.Liew Qi Ying

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    Introduction

    Objective

    Problem Investigated

    Problem Solving

    Further Exploration

    Conclusion

    Reference

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    Cake is a term with a long history (the word is of Viking origin, from the

    Old Norse kaka) and denotes a baked flour confection sweetened with sugar

    or honey; it is mixed with eggs and often, but not invariably, with milk andfat; and it has a porous texture from the mixture rising during cooking. It is

    not surprising that the frontiers between cake and bread, biscuit and bun areindistinct. The progenitor of all is bread in its simplest form. As techniques

    for baking and leavening developed, and eating patterns changed, what were

    originally regarded as forms of bread came to be seen as categories of their

    own and named accordingly. Certain Roman breads, enriched with eggs and

    butter, must have achieved a cakelike consistency and thus approached one

    of these indistinct frontiers.

    Europe and places such as North America where European influence is

    strong have always been the center of cakes. One might even draw a linemore tightly, for English-speaking areas. No other language has a word that

    means exactly the same as the English 'cake.' The continental Europeangateau and torte often contain higher proportions of butter, eggs and

    enriching ingredients such as chocolate, and often lean towards pastry rather

    than cake. Central and East European items such as baba and the

    Easterkulich are likewise different.

    The western tradition of cakes applies little in Asia. In some countries

    western-style cakes have been adopted on a small scale, for example thesmall sponge cakes called kasutera in Japan. But the 'cakes' which are

    important in Asian are quite different from anything occidental for

    examples, see moon cakes and rice cakes of the Philippines.

    The history of cakes, goes a long way back. Among the remains found in

    Swiss lake villages were crude cakes make from roughly crushed gains,

    moistened, compacted and cooked on a hot stone. Such cakes can beregarded as a form of unleavened bread, as the precursor of all modern

    European baked products. Some modern survivors of these mixtures still goby the name 'cake', for instance oatcakes, although these are now considered

    to be more closely related to biscuits by virtue of their flat, thin shape and

    brittle texture. Ancient Egypt was the first culture to show evidence of true

    skill in baking, making many kinds of bread including some sweetened with

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    hone. The Greeks had a form of cheesecake and the Romans developed

    early versions of fruitcakes with raisins, nuts and other fruits. These ended

    up in 14th century Britain. Chaucer mentions immense cakes made for

    special occasions. One was made with 13 kilograms of flour and contained

    butter, cream, eggs, spices, currants and honey.

    Moulds, in the form of cake hoops or pans have been used for forming cakes

    since at least the mid-17th century. Most cakes were eaten accompanied bya glass of sweet wine or tea. At large banquets, elaborately decorated cakes

    might form part of the display, but would probably not be eaten. By the mid-19th century the French were including a separate "sweet" course at the end

    of the meal which might include 'gateau.'

    During the 19th century, technology made the cake-baker's life much easier.

    The chemical raising agent bicarbonate of soda, introduced in the 1840's,followed by baking powder (a dry mixture of bicarbonate of soda with a

    mild acid), replaced yeast, providing a greater leavening power with lesseffort. Another technology breakthrough was more accurate temperature

    controlled ovens.

    In most of NW Europe and North America a well-developed tradition of

    home baking survives, with a huge repertoire of cake recipes developed

    from the basic methods. The ability to bake a good cake was a prized skill

    among housewives in the early to mid-20th century, when many households

    could produce a simple robust, filling 'cut and come again' cake, implyingabundance and hospitality.

    Although the popularity of home baking and the role of cakes in the diet

    have both changed during the 20th century, cakes remain almost ubiquitousin the western world. They have kept their image as 'treats' and maintain

    their ceremonial importance at weddings and birthdays.

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    -produce students who are able to apply concepts and skills in problemsolving

    - to improve the skills of thinking and communicating with the correct grammarand appropriate.

    -promote the intrinsic value such as neat working,systematic, precise and others

    -inculcate the spirit to try and not give up easily

    -make learning more fun, challenging, useful and meaningful

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    Part ICakes come in a variety of forms and flavours and are among favouritedesserts served during special occasions such as birthday parties, Hari Raya,weddings and etc. Cakes are treasured not only because of their wonderfultaste but also in the art of cake baking and cake decorating. Find out howmathematics is used in cake baking and cake decorating and write about your

    findings.

    Part IIBest Bakery shop received an order from your school to bake a 5 kg of roundcake as shown in Diagram 1 for the Teachers Day celebration.

    (Diagram 1)

    1)If a kilogram of cake has a volume of 3800 , and the height of the cake is

    to be 7.0 cm, calculate the diameter of the baking tray to be used to fit the 5kg cake ordered by your school.[Use = 3.142]

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

    a)If the volume of cake remains the same, explore by using different values ofheights, h cm, and the corresponding values of diameters of the baking tray tobe 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 cakes and explainyour answers.

    (ii) suggest the dimensions that you think most suitable for the cake. Givereasons for your answer.

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    (c) (i) Form an equation to represent the linear relation between h and d.Hence, plot a suitable graph based on the equation that you have formed.[You may draw your graph with the aid of computer software.]

    (ii) (a) If Best Bakery received an order to bake a cake where the height of the

    cake is 10.5 cm, use your graph to determine the diameter of the round cakepan required.

    (b) If Best Bakery used a 42 cm diameter round cake tray, use your graph toestimate the height of the cake obtained.

    3) Best Bakery has been requested to decorate the cake with fresh cream.The thickness of the cream is normally set to a uniform layer of about 1cm.

    (a) Estimate the amount of fresh cream required to decorate the cake usingthe dimensions that you have suggested in 2(b)(ii).

    Therefore, amount of fresh cream = 2375 + 1382.23 = 3757.23 cm

    (b) Suggest three other shapes for cake, that will have the same height andvolume as those suggested in 2(b)(ii). Estimate the amount of fresh cream tobe used on each of the cakes.

    (c) Based on the values that you have found which shape requires the leastamount of fresh cream to be used?

    Part III

    Find the dimension of a 5 kg round cake that requires the minimum amount offresh cream to decorate. Use at least two different methods includingCalculus. State whether you would choose to bake a cake of suchdimensions. Give reasons for your answers.

    FURTHER EXPLORATIONBest Bakery received an order to bake a multi-storey cake for Merdeka Daycelebration, as shown in Diagram 2.

    The height of each cake is 6.0 cm and the radius of the largest cake is 31.0

    cm. The radius of the second cake is 10% less than the radius of the firstcake, the radius of the third cake is10% less than the radius of the secondcake and so on.

    (a)Find the volume of the first, the second, the third and the fourth cakes. Bycomparing all these values, determine whether the volumes of the cakes forma number pattern? Explain and elaborate on the number patterns.

    (b) If the total mass of all the cakes should not exceed 15 kg, calculatethe maximum number of cakes that the bakery needs to bake. Verify youranswer using other methods.

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    ReflectionWhile you were conducting the project, what have you learnt? What moralvalues did you practise? Represent your opinions or feelings creativelythrough usage of symbols, illustrations, drawing or even in a song.

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    Part ICakes come in a variety of forms and flavours and are among favouritedesserts served during special occasions such as birthday parties, Hari Raya,weddings and etc. Cakes are treasured not only because of their wonderfultaste but also in the art of cake baking and cake decorating. Find out howmathematics is used in cake baking and cake decorating and write about yourfindings.

    Answer:

    Method ExplanationProgressions To determine total weight/volume of multi-storey cakes with

    proportional dimensions, to estimate total ingredientsneeded for cake-baking, to estimate total amount of creamfor decoration.

    Geomet

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