IF the data about students of the commerce stream in all colleges is represented by a pie chart. What is the central angle of the sector representing college D, to the nearest degree

Options

A. `66^@`
B. `82^@`
C. `88^@`
D. `85^@`

Answer

To find the central angle of the sector representing College D in a pie chart, follow these steps:

### Step-by-Step Solution:

1. **Identify the Total Number of Students**:
- From the problem, we have the number of students in different colleges:
- College A: 400
- College B: 900
- College C: 325
- College D: 275
- Calculate the total number of students:
\[ \text{Total} = 400 + 900 + 325 + 275 = 1900 \]

2. **Determine the Number of Students in College D**:
- The number of students in College D is given as 275.

3. **Calculate the Central Angle for College D**:
- The formula to find the central angle for a sector in a pie chart is:
\[ \text{Central Angle} = \left( \frac{\text{Number of Students in College D}}{\text{Total Number of Students}} \right) \times 360^\circ \]
- Plugging in the values:
\[ \text{Central Angle} = \left( \frac{275}{1900} \right) \times 360 \]

4. **Simplify the Calculation**:
- First, calculate \( \frac{275}{1900} \):
\[ \frac{275}{1900} = 0.1447368421 \quad (\text{approximately}) \]
- Now multiply by 360:
\[ 0.1447368421 \times 360 \approx 52.7 \]

5. **Round to the Nearest Degree**:
- Rounding 52.7 gives us 53 degrees.

6. **Final Answer**:
- The central angle of the sector representing College D is approximately **53 degrees**.