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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

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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

5.1.1 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 of the silo, we first use the volume formula of a cylinder:

V=extπ×(r2)×hV = ext{π} \times (r^2) \times h

Given that the volume is 60 m³ and the height ( (h)) is 7.35 m, we can rearrange the formula to find the radius:

radius2=Vπ×h=603.142×7.35 radius≈2.59811173≈1.61186574 \text{radius}^2 = \frac{V}{\text{π} \times h} = \frac{60}{3.142 \times 7.35}\ \text{radius} \approx \sqrt{2.59811173} \approx 1.61186574\

Thus, the diameter is:

diameter=2×radius≈2×1.61186574≈3.22373048 m\text{diameter} = 2 \times \text{radius} \approx 2 \times 1.61186574 \approx 3.22373048\ m

Step 2

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

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Answer

The total maximum capacity of one silo is:

Total Capacity=4×60 m3=240 m3\text{Total Capacity} = 4 \times 60\ m³ = 240\ m³

Now, converting to gallons:

Total Capacity in gallons=240 m3×1000 ℓ3.7 ℓ/gallon≈64,864.86 gallons\text{Total Capacity in gallons} = \frac{240\ m³ \times 1000\ ℓ}{3.7\ ℓ/gallon} \approx 64,864.86\ gallons

Step 3

5.1.3 Verify, showing ALL calculations, whether she will have enough fertiliser for the wheat field.

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Answer

To find the total amount of fertiliser in the silos:

  1. Calculate the amount available in each silo:

    • Silo 1: 15% of 240 m³ = 0.15 \times 240 = 36 m³
    • Silo 2: ( \frac{1}{4} ) of 240 m³ = 0.25 \times 240 = 60 m³
    • Silo 3 and 4 are empty.

    Total volume available = 36 + 60 = 96 m³

  2. Convert to litres:

96m3=96×1000 ℓ=96,000 ℓ96 m³ = 96 \times 1000\ ℓ = 96,000\ ℓ
  1. Convert to kg (1.3 kg = 1 ℓ):
Total in kg=96,000 kg\text{Total in kg} = 96,000\ kg
  1. Calculate fertiliser needed for wheat field:

Fertilisers needed = 1,055 acres \times 22.65 kg/acre = 23,895.75 kg

Since 96,000 kg > 23,895.75 kg, she will have enough fertiliser for the wheat field.

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