Additional Mathematics

Project Work 2

Written by: ALVIN SOO CHUN KIT I/C Num : Angka Giliran: School : Date :

Alvin Soo Chun Kit

Additional Mathematics Project Work 2

2011

TABLE OF CONTENTS

Num. 1 Part I Part II ~ Question 1 ~ Question 2 (a) ~ Question 2 (b) 2 ~ Question 2 (c) ~ Question 3 (a) ~ Question 3 (b) ~ Question 3 (c) 3 4 Part III Further Exploration Question Page

Alvin Soo Chun Kit

Additional Mathematics Project Work 2

2011

PART I History of cake baking and decorating Although clear examples of the difference between cake and bread are easy to find, the precise classification has always been elusive. For example, banana bread may be properly considered either a quick bread or a cake.The Greeks invented beer as a leavener, frying fritters in olive oil, and cheesecakes using goat's milk. In ancient Rome, basic bread dough was sometimes enriched with butter, eggs, and honey, which produced a sweet and cake-like baked good. Latin poet Ovid refers to the birthday of him and his brother with party and cake in his first book of exile, Tristia.Early cakes in England were also essentially bread: the most obvious differences between a "cake" and "bread" were the round, flat shape of the cakes, and the cooking method, which turned cakes over once while cooking, while bread was left upright throughout the baking process. Sponge cakes, leavened with beaten eggs, originated during the Renaissance, possibly in Spain. Cake decorating is one of the sugar arts requiring mathematics that uses icing or frosting and other edible decorative elements to make otherwise plain cakes more visually interesting. Alternatively, cakes can be moulded and sculpted to resemble three-dimensional persons, places and things. In many areas of the world, decorated cakes are often a focal point of a special celebration such as a birthday, graduation, bridal shower, wedding, or anniversary. Mathematics are often used to bake and decorate cakes, especially in the following actions: y y y y y

Measurement of Ingredients Calculation of Price and Estimated Cost Estimation of Dimensions Calculation of Baking Times Modification of Recipe according to scale

Alvin Soo Chun Kit

Additional Mathematics Project Work 2

2011

PART II 1) 1 kg = 3800 cm3 h = 7 cm 5 kg = 3800 x 5 = 19000 cm3 V = r2h 19000 = 3.142 x r2 x 7 r2 = 19000 3.142 x 7 r2 = 863.872 r = 29.392 cm .

d = 2r d = 58.783 cm 2) Maximum dimensions of cake: d = 60.0 cm h = 45.0 cm a) h/cm 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 d/cm 155.5262519 109.9736674 89.79312339 77.76312594 69.5534543 63.49332645 58.78339783 54.98683368 51.84208396 49.18171919 46.89292932 44.89656169 43.13522122 41.56613923 40.15670556 h/cm 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 d/cm 38.88156297 37.72065671 36.65788912 35.68016921 34.77672715 33.93861056 33.15830831 32.42946528 31.74666323 31.10525037 30.50120743 29.93104113 29.39169891 28.88049994 28.39507881 h/cm 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 d/cm 27.93333944 27.49341684 27.07364537 26.67253215 26.2887347 25.92104198 25.56835831 25.2296896 24.90413158 24.59085959 24.28911983 23.99822167 23.71753106 23.44646466 23.18448477

b) i) h < 7 cm , h > 45 cm This is because any heights lower than 7 cm will result in the diameter of the cake being too big to fit into the baking oven while any heights higher than 45 cm will cause the cake being too tall to fit into the baking oven b) ii) I would suggest the dimensions of the cake to be 29 cm in height and approximately 29 cm in diameter. This is because a cake with these dimensions is more symmetrical and easier to decorate.

Alvin Soo Chun Kit

Additional Mathematics Project Work 2

2011

c) i)

V = r2 h V = 19000 cm3 r = d/2 19000 = 3.142 x (d/2)2 x h d2 = 19000 4 3.142 x (d2/4) .

d2 =

76000 3.142 x h

.

d = 155.53 x h-1/2 log10 d = -1/2 log10 h + log10 155.53

log10 h

1 2 3 4

log10 d

1.691814 1.191814 0.691814 0.191814

c) ii) a) When h =...