Liam and Amy are planning their wedding. Amy wants a four-layer red velvet wedding cake. She must still decide between a cylindrical or rectangular cake as shown on ANNEXURE A. Use ANNEXURE $$ B $$ to answer the questions that follow. P.1.1 Determine the total height of the cylindrical cake in millimetres. A.1.2 The base (bottom) layer of the cylindrical cake has a radius of 14 cm . (a) Determine the diameter of the base layer in cm . (b) Calculate the volume (in $$ \mathrm{cm}^{3} $$ ) of the base layer. You may use the following formula: Volume of a cylinder $$ =\pi imes( ext { radius })^{2} imes $$ height, and using $$ \pi=3,142 $$ 4.1.3 Define the term perimeter. 4.1.4 Calculate the area (in $$ \mathrm{cm}^{2} $$ ) of the base of the pan needed to bake the top layes of the rectangular cake. You may use the following formula: Area $$ = $$ length $$ imes $$ width Aunt Abby will bake the wedding cake. She will be using a recipe from a recipe boo. published in England. NOTE: $$ \qquad $$ $$ 1 \mathrm{~kg}=-2,25 $$ pounds - $$ 1 \mathrm{~m} \ell $$ flour $$ =0,7 \mathrm{~g} $$ flour \$3.2.1. Aunt Abby needs 3 and a half pounds of butter. Determine the mass of butter, in kilogram. 4.2.2 Aunt Abby only has a kitchen scale available. If aunt Abby needs $$ 625 \mathrm{~m} \ell $$ of flour, determine the mass of the flour in gram A.2.3 The cake must be baked at $$ 356^{\circ} \mathrm{F} $$.

Question

Liam and Amy are planning their wedding. Amy wants a four-layer red velvet wedding cake. She must still decide between a cylindrical or rectangular cake as shown on ANNEXURE A. Use ANNEXURE $$ B $$ to answer the questions that follow. P.1.1 Determine the total height of the cylindrical cake in millimetres. A.1.2 The base (bottom) layer of the cylindrical cake has a radius of 14 cm . (a) Determine the diameter of the base layer in cm . (b) Calculate the volume (in $$ \mathrm{cm}^{3} $$ ) of the base layer. You may use the following formula: Volume of a cylinder $$ =\pi 	imes(	ext { radius })^{2} 	imes $$ height, and using $$ \pi=3,142 $$ 4.1.3 Define the term perimeter. 4.1.4 Calculate the area (in $$ \mathrm{cm}^{2} $$ ) of the base of the pan needed to bake the top layes of the rectangular cake. You may use the following formula: Area $$ = $$ length $$ 	imes $$ width Aunt Abby will bake the wedding cake. She will be using a recipe from a recipe boo. published in England. NOTE: $$ \qquad $$ $$ 1 \mathrm{~kg}=-2,25 $$ pounds - $$ 1 \mathrm{~m} \ell $$ flour $$ =0,7 \mathrm{~g} $$ flour \$3.2.1. Aunt Abby needs 3 and a half pounds of butter. Determine the mass of butter, in kilogram. 4.2.2 Aunt Abby only has a kitchen scale available. If aunt Abby needs $$ 625 \mathrm{~m} \ell $$ of flour, determine the mass of the flour in gram A.2.3 The cake must be baked at $$ 356^{\circ} \mathrm{F} $$.

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Let's break down the problem step by step.

### P.1.1: Total Height of the Cylindrical Cake
The total height of the cylindrical cake is not provided in the problem statement. We will need to refer to ANNEXURE A for this information. Since I don't have access to that document, I cannot provide the height. Please provide the height if you have it.

### A.1.2: Base Layer of the Cylindrical Cake
#### (a) Determine the diameter of the base layer in cm.
The diameter $$ d $$ of a circle is given by the formula:
$$
d = 2 \times r
$$
where $$ r $$ is the radius.

Given:
- Radius $$ r = 14 \, \text{cm} $$

Calculating the diameter:
$$
d = 2 \times 14 = 28 \, \text{cm}
$$

#### (b) Calculate the volume (in $$ \mathrm{cm}^{3} $$) of the base layer.
The volume $$ V $$ of a cylinder is given by the formula:
$$
V = \pi \times r^2 \times h
$$
where $$ r $$ is the radius and $$ h $$ is the height. Since we do not have the height, we will express the volume in terms of height $$ h $$.

Given:
- Radius $$ r = 14 \, \text{cm} $$
- Using $$ \pi = 3.142 $$

Calculating the volume:
$$
V = 3.142 \times (14)^2 \times h
$$
$$
V = 3.142 \times 196 \times h
$$
$$
V = 615.592 \times h \, \text{cm}^3
$$

### 4.1.3: Define the term perimeter.
The perimeter of a shape is the total distance around the shape. For a circle, the perimeter is also known as the circumference, which can be calculated using the formula:
$$
C = 2 \pi r
$$

### 4.1.4: Calculate the area (in $$ \mathrm{cm}^{2} $$) of the base of the pan needed to bake the top layers of the rectangular cake.
To calculate the area $$ A $$ of a rectangle, we use the formula:
$$
A = \text{length} \times \text{width}
$$
Since the length and width are not provided, please provide those dimensions to calculate the area.

### Aunt Abby's Butter and Flour Requirements
#### A.2.1: Determine the mass of butter in kilograms.
Aunt Abby needs 3.5 pounds of butter. To convert pounds to kilograms, we use the conversion factor:
$$
1 \, \text{kg} = 2.25 \, \text{pounds}
$$
Thus, to convert pounds to kilograms:
$$
\text{mass in kg} = \frac{\text{mass in pounds}}{2.25}
$$
Calculating the mass of butter:
$$
\text{mass in kg} = \frac{3.5}{2.25} \approx 1.5556 \, \text{kg}
$$

#### A.2.2: Determine the mass of the flour in grams.
Aunt Abby needs 625 mL of flour. Given that $$ 1 \, \text{mL} $$ of flour weighs $$ 0.7 \, \text{g} $$:
$$
\text{mass in grams} = \text{volume in mL} \times 0.7
$$
Calculating the mass of flour:
$$
\text{mass in grams} = 625 \times 0.7 = 437.5 \, \text{g}
$$

### Summary of Results
- Diameter of the base layer: $$ 28 \, \text{cm} $$
- Volume of the base layer: $$ 615.592 \times h \, \text{cm}^3 $$ (height needed)
- Perimeter definition: Total distance around a shape.
- Area of the rectangular cake base: (length and width needed)
- Mass of butter: $$ \approx 1.56 \, \text{kg} $$
- Mass of flour: $$ 437.5 \, \text{g} $$

Please provide any missing information (like the height of the cylindrical cake and dimensions for the rectangular cake) to complete the calculations.
- **Diameter of the base layer:** 28 cm - **Volume of the base layer:** $$ 615.592 \times h \, \text{cm}^3 $$ (where $$ h $$ is the height) - **Perimeter:** Total distance around a shape. - **Area of the rectangular cake base:** Cannot be calculated without length and width. - **Mass of butter:** Approximately 1.56 kg - **Mass of flour:** 437.5 g

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