Problem Description:
The image provided is a pie chart that represents the distribution of time spent on various activities in a day. The activities and their corresponding central angles are as follows:
-
Office work: 135°
-
Sleeping: 105°
-
Watching shows: 45°
-
Exercise: 30°
-
Travelling: 15°
-
Miscellaneous: 30°
The task is to analyze the data and solve any related problem. Since no specific question is mentioned, I will assume the task is to determine the percentage of time spent on each activity.
---
Solution:
#### Step 1: Understand the total angle in a pie chart
A pie chart represents a full circle, which has a total of
360°. Each slice of the pie chart corresponds to a fraction of the total time (or value) represented by the chart.
#### Step 2: Calculate the percentage for each activity
The percentage of time spent on each activity can be calculated using the formula:
\[
\text{Percentage} = \left( \frac{\text{Central angle of the activity}}{360^\circ} \right) \times 100
\]
We will calculate this for each activity:
1.
Office work:
\[
\text{Percentage} = \left( \frac{135^\circ}{360^\circ} \right) \times 100 = 0.375 \times 100 = 37.5\%
\]
2.
Sleeping:
\[
\text{Percentage} = \left( \frac{105^\circ}{360^\circ} \right) \times 100 = 0.2917 \times 100 \approx 29.17\%
\]
3.
Watching shows:
\[
\text{Percentage} = \left( \frac{45^\circ}{360^\circ} \right) \times 100 = 0.125 \times 100 = 12.5\%
\]
4.
Exercise:
\[
\text{Percentage} = \left( \frac{30^\circ}{360^\circ} \right) \times 100 = 0.0833 \times 100 \approx 8.33\%
\]
5.
Travelling:
\[
\text{Percentage} = \left( \frac{15^\circ}{360^\circ} \right) \times 100 = 0.0417 \times 100 \approx 4.17\%
\]
6.
Miscellaneous:
\[
\text{Percentage} = \left( \frac{30^\circ}{360^\circ} \right) \times 100 = 0.0833 \times 100 \approx 8.33\%
\]
#### Step 3: Verify the total percentages
To ensure accuracy, we sum up all the percentages:
\[
37.5\% + 29.17\% + 12.5\% + 8.33\% + 4.17\% + 8.33\% = 100\%
\]
The total is 100%, confirming that our calculations are correct.
---
Final Answer:
\[
\boxed{
\begin{aligned}
&\text{Office work: } 37.5\% \\
&\text{Sleeping: } 29.17\% \\
&\text{Watching shows: } 12.5\% \\
&\text{Exercise: } 8.33\% \\
&\text{Travelling: } 4.17\% \\
&\text{Miscellaneous: } 8.33\%
\end{aligned}
}
\]
Parent Tip: Review the logic above to help your child master the concept of pie chart problems worksheet.
