In the pie chart representing the percentages of students having interest in reading various kinds of books, the central angle of the sector representing students reading novels is `81^@` .What is the percentage of students interested in reading novels ?

Options

A. `15%`
B. `18%`
C. `22 1/2%`
D. `27 1/2%`

Answer

To find the percentage of students interested in reading novels based on the central angle of the sector in a pie chart, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between the angle of the sector and the total angle of the pie chart:**
The total angle in a pie chart is always 360 degrees. The angle of the sector representing the students reading novels is given as 81 degrees.

2. **Set up the formula to find the percentage:**
The formula to calculate the percentage of students interested in reading novels is:
\[ \text{Percentage} = \left( \frac{\text{Angle of sector}}{\text{Total angle}} \right) \times 100 \]
Here, the angle of the sector is 81 degrees, and the total angle is 360 degrees.

3. **Substitute the values into the formula:**
\[ \text{Percentage} = \left( \frac{81}{360} \right) \times 100 \]

4. **Calculate the fraction:**
First, simplify the fraction:
\[ \frac{81}{360} = \frac{81 \div 9}{360 \div 9} = \frac{9}{40} \]

5. **Multiply by 100 to find the percentage:**
\[ \text{Percentage} = \left( \frac{9}{40} \right) \times 100 = \frac{900}{40} = 22.5 \]

6. **Final Answer:**
Therefore, the percentage of students interested in reading novels is **22.5%**.