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

The area of the base of box D is calculated as follows:

Area = Length x Width

The dimensions of box D are:

Length = 1,200 mm = 120 cm Width = 325 mm = 32.5 cm

Thus, the area is:

Area = 120 imes 32.5 = 3,900 cm².

The area of the base of box A is 1,056.25 cm². To find the total area for 24 boxes stacked in 2 layers:

Total area = Area of one box x Number of boxes

Total area = 1,056.25 cm² x 24 = 25,350 cm².

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

Ratio = Length : Width = 600 : 325 = 24 : 13 when simplified.

The outside volume of box E can be calculated as follows:

Let the outside volume = V.

Inside volume = V - (0.0936 x V) = V(1 - 0.0936) = 0.9064V.

Given that the inside volume is approximately 0.299 m³, we calculate V:

0.9064V = 0.299 m³ V ≈ 0.329 m³.

Given that the inside volume of one box is 0.299 m³, the number of boxes that can be filled with 6 m³ of compost is:

Number of boxes = Total volume of compost / Volume of one box

Number of boxes = 6 m³ / 0.299 m³ ≈ 20.06, so approximately 20 boxes.

The total volume for 148 boxes is:

Total volume = 148 x 0.299 m³ = 44.252 m³.

Since compost is delivered in 6 m³ truckloads:

Truckloads needed = Total volume / Volume per truckload = 44.252 m³ / 6 m³ ≈ 7.375, rounded up gives 8 truckloads.

Given the diameter of 10.5 inches, the radius is:

Radius = Diameter / 2 = 10.5 / 2 = 5.25 inches.

Using the formula:

h = \frac{Volume (in cm³)}{\pi \times r^{2}},

we substitute: Volume = 20,000 cm³, Radius = 5.25 inches = 5.25 x 2.54 cm = 13.34 cm. Thus:

h = \frac{20,000}{3.142 \times (13.34)^{2}} \approx 35.8 cm.