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
2,700,000
Step 2
3.1.2 Determine, in kg, the total mass of the carp they caught.
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Answer
The total mass of carp is calculated as follows:
Andrew's carp: 2,375 kg
Duncan's carp: 1.2 kg + 0.75 kg (converted from grams to kilograms)
Total mass = 2,375 kg + 1.2 kg + 0.75 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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Each hole has a length, width, and depth of 0.3 m x 0.3 m x 0.5 m.
Volume of one hole = 0.3 m × 0.3 m × 0.5 m = 0.045 m³
Total volume for 12 holes = 0.045 m³ × 12 = 0.54 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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After digging the holes and preparing the concrete, not all of the mixed concrete was required due to settling and spillage during placement. Additionally, concrete may fill cavities and the actual volume required may be slightly less than anticipated due to variations in hole dimensions.
Step 5
3.2.3 Calculate the mass of river sand needed to make 1 m³ of concrete.
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Answer
To calculate the mass of river sand:
From the mixture, if 0.75 m³ requires 5.5 bags (where one bag = 50 kg):
Total weight of cement = 5.5 bags × 50 kg/bag = 275 kg
Weight of one wheelbarrow of river sand = 102 kg
The required ratio will determine how many wheelbarrows (or their weight) are needed for 1 m³.
Assuming the concrete is approximately made with equal parts, we calculate the amount for 1 m³ based on the required ratios.
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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The side area of each post:
Each post is rectangular (1.6 m length, 0.0125 m width), therefore:
Area = 4 sides × (1.6 m × 0.0125 m)
Total area for all 12 posts = 12 × Area
Step 7
3.3.2 Verify, showing all calculations, whether his statement is VALID.
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Calculate the total area considering both the sides of the posts and post caps. The area of each post side and cap can be calculated, and if the sum matches 52,704 cm², Duncan's statement is validated.
Step 8
3.3.3 Calculate how many litres of paint is needed to paint 52 704 cm².
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Answer
Using the spread rate of 12.46 liter/m²:
Convert area from cm² to m²:
Total area = 52,704 cm² = 5.2704 m²
Litres of paint needed = 5.2704 m² × 12.46 liters/m²
