What is the central angle of the sector corresponding to the expenditure incurred on binding? If a publisher pays ₹20,000 as the printing cost for a certain quantity of books, how... What is the central angle of the sector corresponding to the expenditure incurred on binding? If a publisher pays ₹20,000 as the printing cost for a certain quantity of books, how much will he pay for the books?
Understand the Problem
The question is asking for the calculation of the central angle of a sector in a pie chart based on given expenditures related to book publishing. It involves understanding the relationship between expenditure and angles in a pie chart, as well as understanding percentages and their conversion to degrees.
Answer
The central angle for the printing cost is 72 degrees.
Answer for screen readers
The central angle corresponding to the printing cost is 72 degrees.
Steps to Solve
-
Identify the total percentage
The pie chart represents different expenditures related to book publishing in percentages. The central angle for the entire pie chart represents 360 degrees. -
Determine the percentage for printing cost
According to the pie chart, the percentage corresponding to the printing cost is 20%. -
Calculate the central angle for the printing cost
To find the central angle for the printing cost, use the formula:
$$ \text{Central Angle} = \left( \frac{\text{Percentage}}{100} \right) \times 360 $$
Substituting the value:
$$ \text{Central Angle} = \left( \frac{20}{100} \right) \times 360 = 72 \text{ degrees} $$ -
Final Result
The central angle for the printing cost sector in the pie chart has been computed to be 72 degrees.
The central angle corresponding to the printing cost is 72 degrees.
More Information
In a pie chart, each sector's angle is proportional to the percentage it represents from the total, which is 360 degrees. Thus, calculating the angle for a specific percentage is straightforward using the formula provided.
Tips
- Miscalculating the percentage or total for sectors in the pie chart.
- Forgetting to multiply by 360 when converting percentage to angle.
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