To determine which lake activity has a central angle of [tex]\(39.6^\circ\)[/tex], we first need to understand how central angles are calculated in a circle graph (or pie chart).
1. Understand Proportions:
Each activity's proportion of the total number of campers is calculated by dividing the number of campers for that activity by the total number of campers. For Chipwich Summer Camp, the total number of campers is 100.
2. Proportion for Each Activity:
- Kayaking: [tex]\( \frac{15}{100} = 0.15 \)[/tex]
- Wakeboarding: [tex]\( \frac{11}{100} = 0.11 \)[/tex]
- Windsurfing: [tex]\( \frac{7}{100} = 0.07 \)[/tex]
- Waterskiing: [tex]\( \frac{13}{100} = 0.13 \)[/tex]
- Paddleboarding: [tex]\( \frac{54}{100} = 0.54 \)[/tex]
3. Convert Proportion to Central Angle:
To find the central angle for each activity, we multiply the proportion by the total degrees in a circle, which is 360 degrees.
- Central angle for Kayaking: [tex]\( 0.15 \times 360 = 54^\circ \)[/tex]
- Central angle for Wakeboarding: [tex]\( 0.11 \times 360 = 39.6^\circ \)[/tex]
- Central angle for Windsurfing: [tex]\( 0.07 \times 360 = 25.2^\circ \)[/tex]
- Central angle for Waterskiing: [tex]\( 0.13 \times 360 = 46.8^\circ \)[/tex]
- Central angle for Paddleboarding: [tex]\( 0.54 \times 360 = 194.4^\circ \)[/tex]
4. Identify the Correct Activity:
Upon reviewing the computed central angles, we see that the lake activity with a central angle of [tex]\(39.6^\circ\)[/tex] is Wakeboarding.
So, if a circle graph was constructed from the results, the lake activity that has a central angle of [tex]\(39.6^\circ\)[/tex] is Wakeboarding.
