The pie chart shows how a school sports day, which lasts 3 hours in total, is divided between the opening ceremony, the races and the prize-giving, based on...
Question 1 Report
The pie chart shows how a school sports day, which lasts 3 hours in total, is divided between the opening ceremony, the races and the prize-giving, based on the angle of each sector.
- Work out the number of minutes allocated to the races. (2)
- Write the ratio of the opening ceremony time to the prize-giving time, in its simplest form. (2)
Answer Details
This question tests reading a pie chart: since the full circle (360°) represents the whole event (180 minutes), any sector's time is found by taking that sector's fraction of 360° and applying it to 180 minutes.
- The races sector is 200° out of 360°, so the time for races is \(\frac{200}{360} \times 180 = \) 100 minutes [2].
- The opening ceremony is \(\frac{40}{360} \times 180 = 20\) minutes, and the prize-giving is \(\frac{120}{360} \times 180 = 60\) minutes. The ratio of ceremony time to prize-giving time is \(20:60\), which simplifies to 1:3 [2].
As a check, the three sector times should add back to the total: \(20+100+60=180\) minutes, matching the 3-hour sports day exactly, which confirms the working in both parts.
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