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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): TYPE... 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
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3.1.3 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.
Answer
To find the total area needed:
- Area of one box (box A) = 1 056,25 cm²
- For 24 boxes:
- Total area = 24 x 1 056,25 cm² = 25 350 cm².
- Since they are stacked in a double layer:
- Total area needed = 25 350 cm² / 2 = 12 675 cm².
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3.1.5 A municipality bought 148 type E boxes. The inside volume of a type E box is approximately 0,299 m³. They also ordered compost to fill these boxes. The compost is delivered in 6 m³ truckloads.
Answer
To find the inside volume of the box:
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If the inside volume is 9.36% less than the outside volume, we can set:
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Inside volume = Outside volume x (1 - 0.0936)
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If we denote the outside volume as V, then:
- Inside volume = V x 0.9064 = 0,299 m³.
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From this we can find:
- V = 0,299 m³ / 0.9064 ≈ 0,329 m³.
(b) To find the number of boxes that can be filled with 6 m³ of compost:
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Total volume needed for 148 boxes = 148 x 0,299 m³ = 44,252 m³.
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Number of boxes filled by 6 m³:
- Number of boxes = 6 m³ / 0,299 m³ ≈ 20 boxes.
(c) Minimum number of truckloads:
- Total volume of compost = 44,252 m³:
- Number of truckloads = Total volume / volume per truckload = 44,252 m³ / 6 m³ ≈ 8 truckloads.