thematical literacy p2 grade 12 pre - preparatory
3.2.3 estimate the total surface area of the four walls (excluding the roof). assume each wall is a rectangle. use the given dimensions of the length, height and width.
3.2.4 if painting the inside walls costs r85 per m², calculate the total cost to paint the four inside walls.
3.3 below is a pattern for an apron skirt for a barbie doll. the apron skirt is semi - circular in shape and 4.8 cm long with a lace border.
use the diagram below to answer the question that follows.
3.3.1 determine the width (w) of the lace border.
3.3.2 calculate the total area of the apron skirt. you may use the formula : area of a circle = πr², where π = 3.142

Question

Accepted Answer

### 3.2.3
# Explanation:
## Step1: Identify wall - area formula
For a rectangular wall, the area of one wall is $A = \text{length}\times\text{height}$ or $A=\text{width}\times\text{height}$. Let the length of the room be $l$, the width be $w$ and the height be $h$. The four - wall area $A_{total}$ (excluding the roof) is $2(lh + wh)=2h(l + w)$. But since the dimensions of $l$, $w$ and $h$ are not given in the problem statement, assume $l$, $w$ and $h$ are known values. Let $l = 5m$, $w = 4m$ and $h = 3m$ for illustration purposes.
$$A_{total}=2h(l + w)=2\times3\times(5 + 4)$$
## Step2: Calculate the area
$$2\times3\times(5 + 4)=6\times9 = 54m^{2}$$
# Answer:
If we assume $l = 5m$, $w = 4m$ and $h = 3m$, the total surface area of the four walls (excluding the roof) is $54m^{2}$

### 3.2.4
# Explanation:
## Step1: Recall the cost - calculation formula
The cost $C$ of painting is given by $C=\text{cost per square - meter}\times\text{total area}$. We know from 3.2.3 that the total area $A_{total}$ (assumed to be $54m^{2}$) and the cost per square - meter is $R85$.
$$C = 85\times A_{total}$$
## Step2: Calculate the cost
$$C=85\times54=4590$$
# Answer:
The total cost to paint the four inside walls is $R4590$

### 3.3.1
# Explanation:
## Step1: Analyze the radius relationship
The width $W$ of the lace border is the difference between the outer - radius and the inner - radius of the semi - circular apron. The inner - radius $r = 1.5cm$. Let the outer - radius be $R$. The length of the semi - circular arc of the inner part is $l_{1}=\pi r$ and the length of the semi - circular arc of the outer part is $l_{2}=\pi R$. Since the length of the skirt is given as $4.8cm$, and the length of the skirt is the length of the outer semi - circular arc, $\pi R=4.8$, so $R=\frac{4.8}{\pi}\approx\frac{4.8}{3.142}\approx1.53cm$.
$$W=R - r$$
## Step2: Calculate the width
$$W=\frac{4.8}{3.142}-1.5\approx1.53 - 1.5 = 0.03cm$$
# Answer:
The width $W$ of the lace border is approximately $0.03cm$

### 3.3.2
# Explanation:
## Step1: Recall the area formula for a semi - circle
The area of a full - circle is $A=\pi r^{2}$, so the area of a semi - circle is $A=\frac{1}{2}\pi r^{2}$. The total area of the apron skirt is the area of the outer semi - circle minus the area of the inner semi - circle. The outer - radius $R=\frac{4.8}{\pi}$ and the inner - radius $r = 1.5cm$.
$$A=\frac{1}{2}\pi R^{2}-\frac{1}{2}\pi r^{2}=\frac{1}{2}\pi(R^{2}-r^{2})$$
## Step2: Substitute the values and calculate
$$R=\frac{4.8}{\pi}\approx1.53cm$$, $r = 1.5cm$
$$A=\frac{1}{2}\times3.142\times((1.53)^{2}-(1.5)^{2})$$
$$=\frac{1}{2}\times3.142\times(2.3409 - 2.25)$$
$$=\frac{1}{2}\times3.142\times0.0909$$
$$= 0.143cm^{2}$$
# Answer:
The total area of the apron skirt is approximately $0.143cm^{2}$

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QUESTION IMAGE

Question

Explanation:

3.2.3

Step1: Identify wall - area formula

Step2: Calculate the area

Step1: Recall the cost - calculation formula

Step2: Calculate the cost

Step1: Analyze the radius relationship

Step2: Calculate the width

Answer:

3.2.4