Rian has a factory that manufactures rectangular plant boxes with different sizes - NSC Mathematical Literacy - Question 3 - 2017 - Paper 1

To calculate the area of the base of box D, we use the formula for the area of a rectangle:

$$ext{Area} = ext{Length} imes ext{Width}$$

Substituting the dimensions from the table:

$$ext{Area} = 1200 ext{ mm} imes 325 ext{ mm} = 390000 ext{ mm}²$$

Converting mm² to cm² (1 cm² = 100 mm²):

ext{Area} = rac{390000 ext{ mm}²}{100} = 3900 ext{ cm}²

The total area needed for 24 boxes can be calculated as follows:

1. Calculate the area for a single layer:

   • Area of one box = 1 056,25 cm²
   • Total area for 24 boxes = 1 056,25 cm² × 24 = 25 350 cm²

2. Since they are stacked in a double layer, the total area needed is:

   • Total area = 25 350 cm² × 2 = 50 700 cm²

For box type C, the length is 600 mm and the width is 325 mm. The ratio can be expressed as:

ext{Ratio} = rac{600 ext{ mm}}{325 ext{ mm}} = rac{600}{325} ext{ (simplifying gives)} = rac{24}{13}

To find the inside volume, we first calculate the outside volume using the outer dimensions:

1. Calculate the outside volume of box E:

   • Volume = Length × Width × Height
   • Volume = 1500 mm × 475 mm × 462.5 mm
   • Convert to m³:
   • Volume ≈ 0.32953125 m³

2. Now, calculate 9.36% of the outside volume:

   • 9.36% of 0.32953125 m³ = 0.32953125 × rac{9.36}{100} = 0.030756154 m³

3. Subtract this from the outside volume:

   • Inside Volume = Outside Volume - 9.36%
   • Inside Volume ≈ 0.32953125 m³ - 0.030756154 m³ ≈ 0.298765096 m³ ≈ 0.299 m³ (rounded)

To find the number of boxes that can be filled, use the inside volume calculated:

1. Number of boxes that can be filled =

   • Total compost available = 6 m³
   • Inside volume of one box = 0.299 m³

2. Calculation:

   • Number of boxes = rac{6 ext{ m}³}{0.299 ext{ m}³} ≈ 20.066
   • Therefore, approximately 20 boxes can be filled.

To determine the number of truckloads:

1. Total volume needed for 148 boxes:

   • Total volume = 148 × 0.299 m³ ≈ 44.252 m³

2. Truckloads needed:

   • Truckloads = rac{44.252 m³}{6 m³} ≈ 7.37537
   • Therefore, rounding up, a minimum of 8 truckloads is required.