Mrs Dundee, an Australian farmer, has four silos on her farm in which she stores fertiliser, as shown in the photograph and diagram below. The silos are cylindrical with a roof section. Fertiliser is only stored in the cylindrical part of the silos. The following formula and conversion rates may be used: Volume of a cylinder = π × (radius)² × height; using π = 3,142 1 m³ = 1 000 € 1 m³ = 1 000 litre 1 kg = 1 litre 1 gallon = 3,7 litres 5.1.1 Calculate the diameter of a silo if the volume of the cylindrical part is 60 m³. 5.1.2 Calculate the total maximum capacity (in gallons) of the four silos. 5.1.3 After fertilising all her main fields, Mrs Dundee wants to use the remaining fertiliser for a wheat field, which is 1 055 acres in size. The capacity readings of the four silos are as follows: - Silo 1: 15% full - Silo 2: 1/4 full - Silos 3 and 4: empty Verify, showing ALL calculations, whether she will have enough fertiliser left in her silos for the wheat field if the spread rate is 22,65 kg of fertiliser per acre.

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Mrs Dundee, an Australian farmer, has four silos on her farm in which she stores fertiliser, as shown in the photograph and diagram below - NSC Mathematical Literacy - Question 5 - 2016 - Paper 2

Question 5

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Mrs Dundee, an Australian farmer, has four silos on her farm in which she stores fertiliser, as shown in the photograph and diagram below. The silos are cylindrical ... show full transcript

Worked Solution & Example Answer:Mrs Dundee, an Australian farmer, has four silos on her farm in which she stores fertiliser, as shown in the photograph and diagram below - NSC Mathematical Literacy - Question 5 - 2016 - Paper 2

Step 1

Calculate the diameter of a silo if the volume of the cylindrical part is 60 m³.

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Answer

To find the diameter, we first use the formula for the volume of a cylinder: $V = π × (radius)² × height$ Here, the height is given as 7.35 m, and the volume is 60 m³.

Substituting the values: $60 = 3.142 × (radius)² × 7.35$

Rearranging gives: $(radius)² = \frac{60}{3.142 × 7.35}$ $(radius)² ≈ 2.598111173$

Taking the square root: $radius ≈ 1.611865743$

The diameter is: $diameter = 2 × radius ≈ 3.223731486$ Thus, the diameter of the silo is approximately 3.22 m.

Step 2

Calculate the total maximum capacity (in gallons) of the four silos.

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Answer

To find the total capacity, we first calculate the maximum volume of all four silos:

Each silo has a volume of 60 m³, so: $Total\, volume = 4 × 60 = 240 \, m³$

Now converting cubic meters to gallons: $240 \, m³ × \frac{1 \, gallon}{0.00378541 \, m³} ≈ 63,416.61 \, gallons$ Therefore, the total maximum capacity of the four silos is approximately 63,416.61 gallons.

Step 3

After fertilising all her main fields, Mrs Dundee wants to use the remaining fertiliser for a wheat field, which is 1 055 acres in size.

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Answer

First, we need to determine the total amount of fertiliser needed for 1 055 acres: $Fertiliser\,needed = 1 055 \text{ acres} × 22.65 \text{ kg/acre} ≈ 23,895.75 \, kg$

Now, we calculate the amount of fertiliser left in the silos:

Silo 1: 15% of 60 m³ = 9 m³
Silo 2: 1/4 of 60 m³ = 15 m³
Silos 3 and 4: 0 m³

Total volume available: $Total\, volume = 9 + 15 + 0 + 0 = 24 \, m³$ Converting to litres (1 m³ = 1,000 litres): $24 \, m³ × 1,000 ≈ 24,000 \, litres$

Now converting litres to kg (1 kg = 1 litre): $Total\, stock = 24,000 \, kg$

Comparing available fertiliser with the needed amount: $24,000 \, kg \geq 23,895.75 \, kg$ Hence, Mrs Dundee will have enough fertiliser for her wheat field.

Mrs Dundee, an Australian farmer, has four silos on her farm in which she stores fertiliser, as shown in the photograph and diagram below - NSC Mathematical Literacy - Question 5 - 2016 - Paper 2

Worked Solution & Example Answer:Mrs Dundee, an Australian farmer, has four silos on her farm in which she stores fertiliser, as shown in the photograph and diagram below - NSC Mathematical Literacy - Question 5 - 2016 - Paper 2

Calculate the diameter of a silo if the volume of the cylindrical part is 60 m³.

Calculate the total maximum capacity (in gallons) of the four silos.

After fertilising all her main fields, Mrs Dundee wants to use the remaining fertiliser for a wheat field, which is 1 055 acres in size.

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