A farm's livestock is shown in the pie chart below, with the sector angle marked for each animal. The farm keeps \(200\) animals in total. CowsSheepPigsChic...
Question 1 Report
A farm's livestock is shown in the pie chart below, with the sector angle marked for each animal. The farm keeps \(200\) animals in total.
- Work out the number of cows on the farm. (2)
- Work out the number of pigs on the farm. (2)
Answer Details
In a pie chart, each sector's angle is the same fraction of \(360^\circ\) as that animal's share of the whole farm; measuring the angle marked for cows and for pigs against the full circle converts each into a number of animals.
- The cows' sector spans \(108^\circ\) of the circle: \[ \text{cows} = \frac{108}{360}\times200 = 60 \] [2 marks]
- The pigs' sector spans \(54^\circ\) of the circle: \[ \text{pigs} = \frac{54}{360}\times200 = 30 \] [2 marks]
The cows' sector is exactly double the pigs' sector (\(108^\circ\) against \(54^\circ\)), which is why there are exactly twice as many cows as pigs, \(60\) against \(30\), on the farm.
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