Andrew and Duncan went fishing for carp on a friend's farm - NSC Mathematical Literacy - Question 3 - 2023 - Paper 2

The total mass of all the carp caught is calculated as follows:

• Andrew's carp: 2.375 kg
• Duncan's first carp: 1.2 kg
• Duncan's second carp: 0.750 kg (750 g is converted to kg)

Total mass = 2.375 + 1.2 + 0.750 = 4.325 kg.

The volume of one hole can be calculated using:

Volume = length × width × depth.

Each hole has a side length of 0.3 m and a depth of 0.6 m, so:

Volume of one hole = 0.3 m × 0.3 m × 0.6 m = 0.054 m³.

Total capacity for 12 holes = 12 × 0.054 m³ = 0.648 m³.

Andrew had leftover concrete because the volume of concrete he mixed was based on the calculation for the holes, and it is likely that when he filled the holes, there was some concrete that was not used, resulting in excess due to factors like spillage, shape of the holes, or slight overestimations in the volume.

Using the ratio of ingredients:

If 0.75 m³ of concrete requires 5.5 bags (which is equivalent to the mass of cement), then:

For 1 m³, the mass of cement would be:

Mass of cement for 1 m³ = (5.5 bags / 0.75 m³) × 1 m³ = 7.33 bags.

Given that one level wheelbarrow full of river sand weighs 102 kg, calculate the total sand needed from the ratio:

If the mixture ratio is cement: river sand: stone, calculate the corresponding river sand mass needed for 1 m³.

Each post cap has a base side of 15.24 cm and a height of 2.5 cm. First, calculate the post cap area:

Area of two sides (each side is 125 mm wide):

Area = 2 × (length × width) = 2 × (160 cm × 0.125 cm) = 40 cm².

For areas of post caps convert to cm² and total accordingly for all required painted faces.

Calculate total area (posts + caps) based on the previous findings to check if it tallies with the 52 704 cm² mentioned. Show calculations clearly for validation based on summed areas.

Using the spread rate of paint:

Total area = 52,704 cm² = 5.2704 m².

Required litres = Total area × spread rate = 5.2704 m² × 12.46 litres/m² = Amount needed.