Calculate the radius of a cork and the outside height of a pin board with borders, rounded to the nearest 100 mm.

The diagram shows the diameter of a cylindrical cork is $20 \text{ mm}$.

The radius is half of the diameter.

The radius of one cork is $\boxed{\text{10 mm}}$.

4.1.2

The inner height of the pin board is $309 \text{ mm}$.
The border width is $4 \text{ cm}$ on the top and $4 \text{ cm}$ on the bottom.

The outside height includes the inner height plus the top and bottom borders.

$389 \text{ mm}$ is closer to $400 \text{ mm}$ than to $300 \text{ mm}$.
The outside height of the pin board with the border, rounded to the nearest $100 \text{ mm}$, is $\boxed{\text{400 mm}}$.

4.1.3

The radius $r = 10 \text{ mm} = 0.01 \text{ m}$.
The height $h = 43 \text{ mm} = 0.043 \text{ m}$.
Using the formula: Total surface area of a cylinder = $2 \times 3.142 \times \text{radius}^2 + 2 \times 3.142 \times \text{radius} \times \text{height}$

Lareb collected 53 corks and painted each with 3 layers.

The spread rate is $3 \text{ m}^2$ per litre.

The paint is sold in $125 \text{ ml}$ cans. Convert the volume of paint to ml.

Number of cans needed:

Since you cannot buy a fraction of a can, Lareb must buy 2 cans.

Each can costs R$55.00$.

The total cost of the paint required is $\boxed{\text{R110.00}}$.