The students in Aadi’s class selected one of five sports to participate in during a school sports competition.

He wants to draw a sector graph to show their choices.

He knows that

one-third of the students chose volleyball

three times as many students chose basketball as chose hockey

twice as many students chose football as chose basketball

the same number of students chose football as chose netball.

What should the size of the sector angle for basketball be on Aadi’s graph?

15°

30°

48°

45°

To solve this, let's break down the problem step by step and determine the size of the sector angle for basketball.

### Step 1: Set Variables for Each Sport
Let the number of students who chose hockey be \( h \).

- **Basketball**: We are told that three times as many students chose basketball as chose hockey. Therefore, the number of students who chose basketball is \( 3h \).
- **Football**: We are told that twice as many students chose football as chose basketball, so the number of students who chose football is \( 2 \times 3h = 6h \).
- **Netball**: We are told that the same number of students chose football as chose netball, so the number of students who chose netball is also \( 6h \).
- **Volleyball**: One-third of the students chose volleyball, meaning that the number of students who chose volleyball is \( \frac{1}{3} \) of the total number of students.

### Step 2: Set Up the Total Number of Students
Let's find the total number of students in the class. The total number of students can be expressed as the sum of the number of students participating in each sport:
\[
\text{Total students} = h (\text{hockey}) + 3h (\text{basketball}) + 6h (\text{football}) + 6h (\text{netball}) + \frac{1}{3} \times \text{Total students} (\text{volleyball})
\]
Let the total number of students be \( T \). Then:
\[
T = h + 3h + 6h + 6h + \frac{1}{3}T
\]
Simplifying:
\[
T = 16h + \frac{1}{3}T
\]
To eliminate the fraction, multiply the entire equation by 3:
\[
3T = 48h + T
\]
Subtract \( T \) from both sides:
\[
2T = 48h
\]
Thus, the total number of students is \( T = 24h \).

### Step 3: Determine the Sector Angle for Basketball
The number of students who chose basketball is \( 3h \). The fraction of students who chose basketball is:
\[
\text{Fraction of basketball students} = \frac{3h}{24h} = \frac{1}{8}
\]
The total angle in a circle is \( 360^\circ \). Therefore, the size of the sector angle for basketball is:
\[
\text{Basketball sector angle} = \frac{1}{8} \times 360^\circ = 45^\circ
\]

### Conclusion
The size of the sector angle for basketball on Aadi’s graph should be **45°**.

---

Do you have any questions? Here are some related questions:

1. How would the angle change if twice as many students chose basketball?
2. What is the sector angle for volleyball?
3. If the number of students who chose hockey doubled, what would happen to the basketball angle?
4. How would the sector angles be affected if there were 30 students in the class?
5. How can you represent these relationships in a bar chart instead of a sector graph?

**Tip**: When working with sector graphs, always convert the fraction of the total into a proportion of 360° to find the correct angle.

Learn how to calculate the sector angle for basketball in a sector graph based on student choices in a school sports competition. Understand the mathematical concepts of fractional parts, circle angles, and proportions. Suitable for Grades 6-8.

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