The pie chart below shows the grades for a particular examination that the year 7 students participated in. Use the pie chart to answer the following questions: (a) What is the cen... The pie chart below shows the grades for a particular examination that the year 7 students participated in. Use the pie chart to answer the following questions: (a) What is the central angle of sector D? (b) If there are 200 year 7 students, then how many students received grade A?
Understand the Problem
The question provides a pie chart displaying the grades of year 7 students in an examination. It asks us to determine the central angle of sector D and calculate the number of students who received grade A, given a total of 200 students.
Answer
(a) $72^\circ$ (b) 32
Answer for screen readers
(a) The central angle of sector D is $72^\circ$. (b) The number of students who received grade A is 32.
Steps to Solve
- Calculate the central angle of sector D
A full circle has $360^\circ$. The sector D represents 20% of the pie chart. Therefore, the central angle of sector D is 20% of $360^\circ$: $$ 0.20 \times 360^\circ = 72^\circ $$
- Calculate the number of students who received grade A
There are 200 students in total, and grade A represents 16% of the students. To find the number of students who received grade A, calculate 16% of 200: $$ 0.16 \times 200 = 32 $$
(a) The central angle of sector D is $72^\circ$. (b) The number of students who received grade A is 32.
More Information
A pie chart is often used to represent data in percentages. The total percentage adds up to $100%$, which corresponds to $360^\circ$ in terms of the central angle.
Tips
A common mistake is to confuse percentages with the actual number of students. Remember to convert the percentage into the actual number of students by multiplying the percentage by the total number of students.
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