Question

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.
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

Explanation:

3.2.3

Step1: Identify wall dimensions

Let the length of the room be $l$, width be $w$ and height be $h$. The four - wall surface area (excluding the roof) formula is $2h(l + w)$. But since no dimensions are given in the problem statement for the room's length, width and height, we assume the length is $l$, width is $w$ and height is $h$. The surface area $A=2h(l + w)$.

Step1: Recall surface area from 3.2.3

The surface area of the four walls is $A = 2h(l + w)$.

Step2: Calculate cost

The cost per square - meter is R85. So the total cost $C$ to paint the four walls is $C=85\times2h(l + w)$.

Step1: Analyze the apron - skirt diagram

The length of the outer semi - circular arc of the lace border is half of the circumference of the outer circle, and the length of the inner semi - circular arc of the apron body is half of the circumference of the inner circle. The length of the outer semi - circular arc $L_{outer}=\pi R$ and the length of the inner semi - circular arc $L_{inner}=\pi r$, where $R$ is the outer radius and $r$ is the inner radius. The width $W$ of the lace border is the difference between the outer radius and the inner radius. Given the length of the skirt (which is the outer radius) $R = 4.8$ cm and the inner radius $r = 1.5$ cm. So $W=R - r$.

Step2: Substitute values

$W=4.8−1.5$.

Answer:

$2h(l + w)$

3.2.4