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A farmer keeps sheep in a rectangular field measuring 120m by 180m - OCR - GCSE Maths - Question 9 - 2023 - Paper 1

Question 9

A farmer keeps sheep in a rectangular field measuring 120m by 180m. The farmer can keep up to 20 sheep per hectare in the field. 1 hectare is 10000 square metres. Wo... show full transcript

Worked Solution & Example Answer:A farmer keeps sheep in a rectangular field measuring 120m by 180m - OCR - GCSE Maths - Question 9 - 2023 - Paper 1

Step 1

Step 1: Calculate the area of the field

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Answer

To find the area of the rectangular field, use the formula:

$ext{Area} = ext{length} imes ext{width}$

Substituting in the given dimensions:

$ext{Area} = 120 ext{m} imes 180 ext{m} = 21600 ext{m}^2$

Step 2

Step 2: Convert the area from square metres to hectares

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Answer

Since 1 hectare is equivalent to 10000 square metres, convert the area:

$ext{Area in hectares} = \frac{21600 ext{m}^2}{10000 ext{m}^2/ ext{hectare}} = 2.16 ext{hectares}$

Step 3

Step 3: Calculate the maximum number of sheep

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Answer

Given that the farmer can keep up to 20 sheep per hectare, the maximum number of sheep can be computed as:

$ext{Maximum sheep} = 20 ext{ sheep/hectare} \times 2.16 ext{ hectares} = 43.2 ext{ sheep}$

Since the number of sheep must be a whole number, rounding down gives:

Therefore, the maximum number of sheep the farmer can keep is 43.

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