The diagram shows a triangular field PQR which is used to grow organic carrots. PQ = 100 m, PR = 80 m and angle RPQ = 30°. In recent years, an average of 2.5 kg of carrots has been harvested from each square metre of the field. (a) Use this information to work out the total mass of carrots that might have been harvested from the field in 2019. (b) Why might the answer to part (a) be unreliable?

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The diagram shows a triangular field PQR which is used to grow organic carrots - OCR - GCSE Maths - Question 18 - 2020 - Paper 1

Question 18

The diagram shows a triangular field PQR which is used to grow organic carrots. PQ = 100 m, PR = 80 m and angle RPQ = 30°. In recent years, an average of 2.5 kg of... show full transcript

Worked Solution & Example Answer:The diagram shows a triangular field PQR which is used to grow organic carrots - OCR - GCSE Maths - Question 18 - 2020 - Paper 1

Step 1

Calculate the area of triangle PQR

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Answer

To find the area of triangle PQR, we can use the formula for the area of a triangle given by:

$\text{Area} = \frac{1}{2} \times b \times h$

Where:

b is the base (PQ)
h is the height

Since we know angle RPQ and sides, we can apply the sine rule or the area formula involving sine:

$\text{Area} = \frac{1}{2} \times PQ \times PR \times \sin(RPQ)$
Substituting the values:
$\text{Area} = \frac{1}{2} \times 100 \times 80 \times \sin(30°)$
Knowing that ( \sin(30°) = \frac{1}{2} ), we have:

$\text{Area} = \frac{1}{2} \times 100 \times 80 \times \frac{1}{2} = 1000 \text{ m}^2$

Step 2

Calculate the total mass of carrots harvested

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Answer

To find the total mass of carrots harvested from the field, we multiply the area by the average mass of carrots harvested per square metre:

$\text{Total mass} = \text{Area} \times \text{average mass}$

Substituting the known values:

$\text{Total mass} = 1000 \text{ m}^2 \times 2.5 \text{ kg/m}^2 = 2500 \text{ kg}$

Step 3

Why might the answer to part (a) be unreliable?

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Answer

There are several reasons why the answer to part (a) might be unreliable:

Variability in Crop Yield: The average figure of 2.5 kg may vary significantly due to factors such as weather conditions, soil quality, plant diseases, and farming practices.
Data Limitations: If the data on carrot yields is based on a limited sample or outdated information, it might not accurately reflect current conditions.
Measurement Errors: Errors in measuring the area of the field or the yields can lead to inaccurate estimates.
External Factors: Economic factors or changes in agricultural practices can also influence the yield and harvesting efficiency.

The diagram shows a triangular field PQR which is used to grow organic carrots - OCR - GCSE Maths - Question 18 - 2020 - Paper 1

Worked Solution & Example Answer:The diagram shows a triangular field PQR which is used to grow organic carrots - OCR - GCSE Maths - Question 18 - 2020 - Paper 1

Calculate the area of triangle PQR

Calculate the total mass of carrots harvested

Why might the answer to part (a) be unreliable?

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