To solve this problem, we need to determine the central angles for each lake activity when constructing a circle graph (pie chart). Here are the detailed steps:
1. Find the total number of campers:
Sum up the number of campers for all the activities.
[tex]\[
\text{Total campers} = 15 (\text{Kayaking}) + 11 (\text{Wakeboarding}) + 7 (\text{Windsurfing}) + 13 (\text{Watersking}) + 54 (\text{Paddleboarding}) = 100
\][/tex]
2. Calculate the central angle for each activity:
The central angle for an activity in a circle graph can be found by:
[tex]\[
\text{Central Angle} = \left( \frac{\text{Number of Campers for activity}}{\text{Total Campers}} \right) \times 360^\circ
\][/tex]
- For Kayaking:
[tex]\[
\text{Central Angle} = \left( \frac{15}{100} \right) \times 360^\circ = 54^\circ
\][/tex]
- For Wakeboarding:
[tex]\[
\text{Central Angle} = \left( \frac{11}{100} \right) \times 360^\circ = 39.6^\circ
\][/tex]
- For Windsurfing:
[tex]\[
\text{Central Angle} = \left( \frac{7}{100} \right) \times 360^\circ = 25.2^\circ
\][/tex]
- For Waterskiing:
[tex]\[
\text{Central Angle} = \left( \frac{13}{100} \right) \times 360^\circ = 46.8^\circ
\][/tex]
- For Paddleboarding:
[tex]\[
\text{Central Angle} = \left( \frac{54}{100} \right) \times 360^\circ = 194.4^\circ
\][/tex]
3. Determine which activity has a central angle of approximately 46 degrees:
Looking at the calculated angles, we see:
- Kayaking: 54.0 degrees
- Wakeboarding: 39.6 degrees
- Windsurfing: 25.2 degrees
- Waterskiing: 46.8 degrees
- Paddleboarding: 194.4 degrees
The activity with a central angle closest to 46 degrees is Waterskiing, with a central angle of 46.8 degrees.
Hence, the lake activity that has a central angle of approximately 46 degrees is Waterskiing.
