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 find the length of decorative ribbon for one rectangular vase, we use the formula:

$$Length~of~decorative~ribbon = 2 \times (length + width) + 1$$

Substituting the values, we get:

$$= 2 \times (10~cm + 6~cm) + 1 = 2 \times (16~cm) + 1 = 32~cm + 1 = 33~cm$$

The volume of the cylindrical vase can be calculated using the formula:

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

Given the diameter is 12 cm, the radius will be:

$$Radius = \frac{12~cm}{2} = 6~cm$$

Now substituting the values:

$$= 3,142 \times (6~cm)^2 \times 28~cm = 3,142 \times 36~cm^2 \times 28~cm \approx 3,167.136~cm^3$$

The volume of sand filled is:

$$Volume~of~sand = 1 680~cm^3 \times 0.45 = 756~cm^3$$

Now, using the density of sand which is 1.53 g/cm³, the mass of sand in grams is:

$$Mass = 756~cm^3 \times 1.53~g/cm^3 \approx 1 156.68~g$$

Converting grams to kilograms:

$$Mass~in~kg = \frac{1 156.68}{1000} \approx 1.16~kg$$

Using the formula for the area of a triangle:

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

Substituting in the values:

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

We first find the total surface area using the formula:

$$Total~surface~area = 2 \times (area~of~triangular~face) + 3 \times (length \times width)$$

Substituting the values from the previous calculations:

$$= 2 \times 6.928~cm^2 + 3 \times (6~cm \times 4~cm) = 13.856~cm^2 + 72~cm^2 = 85.856~cm^2$$

First, we determine the average time in minutes to cover one box:

$$Average~time~for~one~box = \frac{30~minutes}{20} = 1.5~minutes$$

Now converting minutes to seconds:

$$1.5~minutes = 1.5 \times 60~seconds = 90~seconds$$