Question

The given pie chart shows the percentage of various crops. Which of the following is the angle sector by the sugarcane category?

• A. 90\(^{\circ}\)
• B. 63\(^{\circ}\)
• C. 36\(^{\circ}\)
• D. 10\(^{\circ}\)

Hint:

Remember that 10% of any number is simply obtained by shifting the decimal point one place to the left.
Since the total angle of a circle is 360\(^{\circ}\), 10% of it is immediately 36\(^{\circ}\).

Answer 1

The Correct Option is C

•

Step 1: Understanding the Question: This question involves converting percentage values from a pie chart into central sector angles.
We must first find the percentage representing Sugarcane and then convert it into degrees of a circle.

•

Step 2: Key Formula or Approach:
1. The sum of all percentages in a pie chart is 100%.
2. Therefore:
\[ \text{Sugarcane Percentage} = 100\% - \sum (\text{Percentages of all other categories}) \]
3. The total central angle of a circle is 360\(^{\circ}\).
4. To convert any percentage \(P\) to a sector angle \(\theta\):
\[ \theta = \frac{P}{100} \times 360^{\circ} \]

•

Step 3: Detailed Explanation:
- Let us sum the given percentages of all other crops from the chart:
- Rice = 49%
- Pulses = 18%
- Wheat = 23%
Summing these percentages:
\[ \text{Sum} = 49\% + 18\% + 23\% = 90\% \]
- Now, let us calculate the percentage for Sugarcane:
\[ \text{Sugarcane \%} = 100\% - 90\% = 10\% \]
- Next, we convert this 10% into a sector angle:
\[ \text{Sector Angle} = \frac{10}{100} \times 360^{\circ} \]
\[ \text{Sector Angle} = 0.10 \times 360^{\circ} = 36^{\circ} \]

•

Step 4: Final Answer: The sector angle of the sugarcane category is 36\(^{\circ}\), matching option (C).