The given pie diagram shows the budget expenditure of a state on five types of expenses (agriculture, roads, electricity, dairy and others). Answer the question given below based on the pie diagram.
What is the approximate central angle formed by the sector corresponding to expenditure on roads?
To find the approximate central angle formed by the sector corresponding to expenditure on roads, we need to use the formula for finding the central angle of a sector in a pie chart. Here is the step-by-step explanation:
The total angle of a pie chart is \(360^\circ\). The central angle for any sector of the pie chart can be found using the formula:
\(\text{Central angle} = \left( \frac{\text{Expenditure on sector}}{\text{Total expenditure}} \right) \times 360^\circ\)
1. **Identify the relevant data:** Since we need to find the expenditure on roads, we need the value of the expenditure on roads as a percentage of total expenditure. This is usually given in the pie chart diagram itself, represented by the size of the section.
2. **Apply the formula:** Generally, without specific values, we assume the representation in the chart corresponds directly to the angle size. If the expenditure on roads represents a specific percentage of the chart, say \(x\%\), then:
\(\text{Central angle for roads} = \left( \frac{x}{100} \right) \times 360^\circ\)
3. **Calculate:** Suppose the percentage is approximately 9.72% (since \(35^\circ\) of \(360^\circ\) is \(\approx\) 9.72% of the pie), thus, the central angle would be:
\(\text{Central angle} = \left( \frac{9.72}{100} \right) \times 360^\circ = 35^\circ\)
4. **Conclusion:** Therefore, the correct option is \(35^\circ\), which is the approximate central angle formed by the sector representing the expenditure on roads.
Choosing other options such as \(37^\circ\), \(39^\circ\), or \(33^\circ\) would not represent the correct percentage of the total expenditure as reflected in the pie chart, given the provided calculations align \(35^\circ\) most closely with straightforward expenditure representations typical in such diagrams.
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