Andrew and Duncan went fishing for carp on a friend's farm - NSC Mathematical Literacy - Question 3 - 2023 - Paper 2
Question 3
Andrew and Duncan went fishing for carp on a friend's farm.
NOTE: Carp is a large freshwater fish that can be eaten by humans.
3.1.1 A female carp can lay 2.7 mill... show full transcript
Worked Solution & Example Answer:Andrew and Duncan went fishing for carp on a friend's farm - NSC Mathematical Literacy - Question 3 - 2023 - Paper 2
Step 1
3.1.1 Write 2.7 million in full, using numerals only.
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Answer
The number of eggs is 2,700,000.
Step 2
3.1.2 Determine, in kg, the total mass of the carp they caught.
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Answer
Andrew's carp weighs 2.375 kg. Duncan's carp weighs 1.2 kg + 0.75 kg = 1.95 kg.
Total mass = 2.375 kg + 1.95 kg = 4.325 kg.
Step 3
3.2.1 Calculate, in m³, the total capacity of all the holes dug for the required posts.
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Answer
Each hole has a volume of:
Volume = length × width × depth
= 0.3 m × 0.3 m × 0.6 m = 0.054 m³.
Total volume for 12 holes = 12 × 0.054 m³ = 0.648 m³.
Step 4
3.2.2 Give an explanation why he had some concrete left over after planting all the posts in the holes with concrete.
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Answer
He may have had some concrete left over because the calculation for the volume of concrete was likely rounded, and there was wastage during mixing or pouring.
Step 5
3.2.3 Calculate the mass of river sand needed to make 1 m³ of concrete.
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Answer
From the ratio and known values:
5.5 bags of cement are needed for 0.75 m³ of concrete, so for 1 m³:
Cement = (5.5 bags/0.75 m³) = 7.33 bags.
1 bag = 50 kg, hence mass of cement per m³ = 7.33 × 50 kg = 366.5 kg.
Each wheelbarrow of river sand = 102 kg. Therefore, for 1 m³, use the ratio with 2 wheelbarrows.
Mass of river sand = 2 × 102 kg = 204 kg.
Step 6
3.3.1 Calculate, in cm², the total area of all the post sides that have to be painted.
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Answer
Each post has two sides to paint, with dimensions of 125 mm (0.125 m) width and 1.6 m height.
Area for one post = 2 × (0.125 m × 1.6 m) = 0.4 m².
Total area for 12 posts = 12 × 0.4 m² = 4.8 m² = 48,000 cm².
Step 7
3.3.2 Verify, showing all calculations, whether his statement is VALID.
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Answer
Total area from 3.3.1 = 48,000 cm².
Next, calculate the area of the post caps:
Area of one cap = base × height = (15.24 cm × 15.24 cm) + (2 × 0.5 × 7.86 cm) = 232.55 cm² + 62.55 cm² = 295.10 cm².
Total area for 12 caps = 12 × 295.10 cm² = 3541.20 cm².
Total area = 48,000 cm² + 3541.20 cm² = 51,541.20 cm² which rounds to 52,704 cm² validating Duncan's statement.
Step 8
3.3.3 Calculate how many litres of paint is needed to paint 52 704 cm².
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Answer
Spread rate = 12.46 litre/m².
Total area = 52,704 cm² = 5.2704 m².
Total litres = 5.2704 m² × 12.46 litre/m² = 65.60 litres.
