Math Problem Statement

Buna göre bu sitenin tüm üyelerinin yaş gruplarına göre dağılımını gösteren daire grafiğinde 18 yaş ve altı kişileri gösteren daire diliminin merkez açısı kaç derecedir?

Solution

To solve the problem based on the given pie charts:

The goal is to calculate the central angle for the 18 years old and under age group across all members. We are provided with three pie charts that give the following information:

  1. Chart 1: Gender Distribution

    • Males occupy 216216^\circ of the total 360360^\circ.
    • This implies the percentage of males is 216360=60%\frac{216^\circ}{360^\circ} = 60\%.
    • Therefore, females occupy 40%40\% of the members.
  2. Chart 2: Age Distribution of Male Members

    • 18 years old and under = 1818^\circ.
    • This means 18360×100=5%\frac{18^\circ}{360^\circ} \times 100 = 5\% of males are 18 years or younger.
  3. Chart 3: Age Distribution of Female Members

    • 18 years old and under = 1818^\circ.
    • Similar to males, 18360×100=5%\frac{18^\circ}{360^\circ} \times 100 = 5\% of females are 18 years or younger.

Total Contribution of 18 Years Old and Under Group

We need to find the overall percentage of members 18 years and under, combining the data from both male and female members:

  • Males make up 60%60\% of the total members, and 5%5\% of them are 18 or younger, so 0.60×0.05=0.030.60 \times 0.05 = 0.03 or 3%3\% of the total population are males aged 18 or younger.
  • Females make up 40%40\% of the total members, and 5%5\% of them are 18 or younger, so 0.40×0.05=0.020.40 \times 0.05 = 0.02 or 2%2\% of the total population are females aged 18 or younger.

Thus, the total percentage of members aged 18 and under is: 3%+2%=5%3\% + 2\% = 5\%

Central Angle for the Age Group

The total angle of a pie chart is 360360^\circ. To find the central angle corresponding to 5% of the total population: 5100×360=18\frac{5}{100} \times 360^\circ = 18^\circ

Thus, the central angle is 18\boxed{18^\circ}, which corresponds to option D.


Do you need further clarification, or would you like details on the steps? Here are five additional related questions you might consider:

  1. How do you calculate percentages from pie charts?
  2. How can you combine data from two different charts?
  3. What is the formula for calculating a central angle from a percentage?
  4. How would the answer change if the age distribution of males and females was different?
  5. What other interpretations can be made from these pie charts?

Tip: Always ensure that the total angles or percentages in pie charts sum up to 360360^\circ or 100%100\%, respectively.

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Math Problem Analysis

Mathematical Concepts

Percentage
Central Angle
Pie Charts

Formulas

Central Angle = (Percentage / 100) × 360°

Theorems

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Suitable Grade Level

Grades 9-11