https://file.aiquickdraw.com/mathbot/file/1727092588330j2ti85n5.jpg

Let's analyze the pie chart and solve the given questions.

### Given:
- Total number of students = 120
- Proportions from the pie chart:
  - **Strawberry** = \( \frac{1}{3} \)
  - **Vanilla** = \( \frac{1}{10} \)
  - **Chocolate** = \( \frac{1}{6} \)
  - **Black Forest** = Remaining portion of the chart.

### (i) Find the central angle of the sector representing **strawberry** and **vanilla** flavors.

The total angle of the pie chart is 360°. The central angle for each flavor is calculated using:
\[
\text{Central Angle} = \left( \text{Proportion} \right) \times 360°
\]

- **Strawberry** \( \left( \frac{1}{3} \right) \):
  \[
  \text{Central Angle of Strawberry} = \frac{1}{3} \times 360° = 120°
  \]

- **Vanilla** \( \left( \frac{1}{10} \right) \):
  \[
  \text{Central Angle of Vanilla} = \frac{1}{10} \times 360° = 36°
  \]

### (ii) Find the percentage of students who like **Black Forest** flavor.

First, we need to determine the fraction of students who prefer Black Forest. The sum of all other flavors' proportions is:
\[
\frac{1}{3} (\text{Strawberry}) + \frac{1}{10} (\text{Vanilla}) + \frac{1}{6} (\text{Chocolate})
\]
To add these fractions, find a common denominator:
\[
\frac{1}{3} = \frac{10}{30}, \quad \frac{1}{10} = \frac{3}{30}, \quad \frac{1}{6} = \frac{5}{30}
\]
Adding them:
\[
\frac{10}{30} + \frac{3}{30} + \frac{5}{30} = \frac{18}{30} = \frac{3}{5}
\]
Thus, the remaining portion for **Black Forest** is:
\[
1 - \frac{3}{5} = \frac{2}{5}
\]
Now, to find the percentage:
\[
\text{Percentage of Black Forest} = \frac{2}{5} \times 100 = 40\%
\]

### (iii) What is the probability of choosing **chocolate** flavor?

The probability of choosing chocolate is the proportion for **chocolate**, which is \( \frac{1}{6} \).

Thus, the probability is:
\[
P(\text{Chocolate}) = \frac{1}{6}
\]

### Summary of Answers:
1. **Central Angle of Strawberry** = 120°
   **Central Angle of Vanilla** = 36°
2. **Percentage of Black Forest** = 40%
3. **Probability of Chocolate** = \( \frac{1}{6} \)

Would you like further details or explanations on any of these? 

Here are five related questions for further practice:
1. How would the central angle change if the proportion of vanilla increased to \( \frac{1}{5} \)?
2. What is the probability of choosing either strawberry or chocolate flavor?
3. If 15 more students were added, how would the proportions change?
4. What is the percentage of students who do not like strawberry?
5. If a new flavor were added, how would the pie chart adjust?

**Tip:** When working with fractions and percentages, always verify proportions add up to 100% to ensure accuracy.

There are 120 students in a hostel. The pie chart shows the proportion of students who love various flavours of cakes. Study the graph and answer the following questions: (i) Find the central angle of sector representing strawberry and vanilla flavours. (ii) Find the percentage of black forest. (iii) What is the probability of choosing chocolate flavour among all the flavours?

Solve pie chart problems related to cake flavours with 120 students. Find the central angle for strawberry and vanilla, calculate the percentage of black forest lovers, and determine the probability of choosing chocolate flavour.

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