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 given dimensions:

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

To convert square millimeters to square centimeters:

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

The area of one box A is 1 056,25 cm². To find the total area needed for 24 boxes stacked in a double layer, we first calculate the area for 12 boxes:

$ext{Total Area} = 12 imes 1 056,25 ext{ cm}^2 = 12 675 ext{ cm}^2$

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

ext{Ratio} = rac{600}{325} = rac{24}{13}

Let V be the outside volume of a type E box. The inside volume is given by:

$ext{Inside Volume} = V imes (1 - 0,0936)$

Thus, we find:

0,299 = V imes 0,9064 \\ V = rac{0,299}{0,9064} \\ V ext{ (outside volume)} ext{ is approximately } 0,32953125 ext{ m}^3

Given that the inside volume of one box is approximately 0,299 m³, the number of boxes that can be filled with 6 m³ of compost is:

ext{Number of boxes} = rac{6}{0,299} ext{ (approx.)} \\ ext{Total Boxes} = 20.066 ext{ (approximately 20 boxes)}

To fill 148 type E boxes with an inside volume of 0,299 m³, the total volume needed is:

$ext{Total Volume} = 148 imes 0,299 ext{ m}^3 = 44,252 ext{ m}^3$

With compost delivered in 6 m³ truckloads, the number of truckloads required is:

ext{Truckloads} = rac{44,252}{6} ext{ (approx.)} \\ ext{Truckloads} = 7.375 ext{ (rounded up to 8)}