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

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Rian has a factory that manufactures rectangular plant boxes with different sizes. A table showing boxes with different sizes (all external dimensions in mm): | TY... show full transcript

Worked Solution & Example Answer:Rian has a factory that manufactures rectangular plant boxes with different sizes - NSC Mathematical Literacy - Question 3 - 2017 - Paper 1

Step 1

Write down the letter (A–E) of the type of plant box that is a cube.

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Answer

The type of plant box that is a cube is A (since all dimensions are equal: 325 mm x 325 mm x 225 mm).

Step 2

Calculate the area (in cm²) of the base of box D.

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Answer

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

extArea=extLengthimesextWidth=1,200extmmimes325extmm=390,000extmm2extConverttocm2:390,000extmm2=39,000extcm2 ext{Area} = ext{Length} imes ext{Width} = 1,200 ext{ mm} imes 325 ext{ mm} = 390,000 ext{ mm}^2 \\ ext{Convert to cm}^2: \\ 390,000 ext{ mm}^2 = 39,000 ext{ cm}^2

Step 3

The area of the base of box A is 1 056,25 cm². Determine the total area (in cm²) needed to store 24 of these boxes if they are stacked on top of each other in a double layer.

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Answer

The area of 24 boxes in a double layer (which means 12 boxes in each layer) is:

extTotalArea=1,056.25extcm2imes24=25,350extcm2extAreaneededinonelayer=25,350extcm2÷2=12,675extcm2 ext{Total Area} = 1,056.25 ext{ cm}^2 imes 24 = 25,350 ext{ cm}^2 \\ ext{Area needed in one layer} = 25,350 ext{ cm}^2 \div 2 = 12,675 ext{ cm}^2

Step 4

Determine, for box type C, the ratio of the length of the box to the width of the box in simplified form.

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Answer

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

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

Step 5

The inside volume of a box is 9,36% less than the outside volume, which shows how the approximated inside volume was calculated.

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Answer

Let the outside volume be denoted as V. The inside volume is given by:

extInsideVolume=V−(0.0936imesV)=V(1−0.0936)=0.9064V ext{Inside Volume} = V - (0.0936 imes V) = V(1 - 0.0936) = 0.9064V

Since for type E box, the inside volume is approximately 0.299 m³, we can calculate:

extVolume(V)=0.2990.9064extm3≈0.3293extm3 ext{Volume}(V) = \frac{0.299 }{0.9064} ext{ m}^3 \approx 0.3293 ext{ m}^3

Step 6

Calculate the number of boxes that can be filled with 6 cubic metres of compost.

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Answer

The total volume of compost is 6 m³. The volume needed for one type E box is 0.299 m³:

extNumberofboxes=60.299≈20.06⇒approximately 20 boxes ext{Number of boxes} = \frac{6}{0.299} \approx 20.06\Rightarrow \text{approximately 20 boxes}

Step 7

Determine the minimum number of truckloads of compost required to fill ALL the boxes.

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Answer

To find the total volume for 148 type E boxes:

extTotalVolume=148imes0.299=44.252extm3 ext{Total Volume} = 148 imes 0.299 = 44.252 ext{ m}^3

Using 6 m³ per truckload:

extTruckloads=44.2526≈7.375⇒approximately 8 truckloads ext{Truckloads} = \frac{44.252}{6} \approx 7.375\Rightarrow \text{approximately 8 truckloads}

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