Happy Life High School makes table centrepieces, each consisting of four balloons in a vase filled with sand, for the 2017 Ball - NSC Mathematical Literacy - Question 3 - 2017 - Paper 1

To calculate the length of the decorative ribbon, we can use the formula provided:

$\text{Length of decorative ribbon} = 2 \times (\text{length} + \text{width}) + 1$

Substituting the values:

$= 2 \times (10 + 6) + 1 = 2 \times 16 + 1 = 33 \text{ cm}$

The formula for the volume of a cylinder is given as:

$\text{Volume} = \pi \times (\text{radius})^2 \times \text{height}$

First, we find the radius from the diameter:

$\text{Diameter} = 12 \text{ cm} \Rightarrow \text{Radius} = \frac{12}{2} = 6 \text{ cm}$

Then substituting the values into the formula:

$= 3.142 \times (6)^2 \times 28 \\ = 3.142 \times 36 \times 28 = 3,167.136 \text{ cm}^3$

The volume of the rectangular vase is 1680 cm³. Since 45% of it is filled with sand, we first calculate the volume of sand:

$\text{Volume of sand} = 1,680 \times 0.45 = 756 \text{ cm}^3$

Given that the mass of 1 cm³ of sand is 1.53 g, we can calculate the mass:

$\text{Mass} = 756 \times 1.53 \approx 1156.68 \text{ grams} = 1.16 \text{ kg}$

Using the formula for the area of a triangle:

$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$

Substituting the values:

$= \frac{1}{2} \times 4 \times 3.464 = 6.928 \text{ cm}^2$

To calculate the total surface area of the triangular prism:

$\text{Total surface area} = 2 \times \text{area of triangular face} + 3 \times \text{length} \times \text{width}$

Substituting the area of the triangular face:

$= 2 \times 6.928 + 3 \times 6 \times 4$

$= 13.856 + 72 = 85.856 \text{ cm}^2$

If it takes 30 minutes to cover 20 boxes, the time for one box is:

$\text{Average time} = \frac{30 \text{ minutes}}{20} = 1.5 \text{ minutes}$

To convert this into seconds:

$1.5 \text{ minutes} \times 60 \text{ seconds/minute} = 90 \text{ seconds}$