Addmath Project Work

Part 1

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 minimum or maximum, amount of cream needed for decorating, to estimate minimum or maximum 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 2

1) Given 1 kg of cake has volume 3800 cm³, and h is 7 cm, so find the d. Volume of 5 kg = Base area of cake x Height of cake 3800 x 5 = (3.142) (d/2)² x 7 19000 / 7 (3.142) = (d/2)² 863.872 = (d/2)² d/2 = 29.392 d = 58.784

2) Given the inner dimensions of oven : 80 cm length, 60 cm width, 45 cm height

a) Find corresponding values of d with different values of h, and tabulate the answers. First, form the formula for d in terms of h by using the above formula for volume of cake, V = 19000, that is : 19000 = (3.142)(d/2)²h 19000/(3.142)h = d²/4 24188.415/h = d² d = 155.53/√h

|Height, h (cm) |Diameter, d (cm) |
|1.0 |155.53 |
|2.0 |109.98 |
|3.0 |89.80 |
|4.0 |77.77 |
|5.0