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Solved on Feb 16, 2024

Find the central angle (in degrees) for the Drums sector in a circle graph displaying the number of students playing instruments: Drums 88, Trumpet 1111, Guitar 99, Violin 88.

STEP 1

Assumptions
1. The total number of students in the band is the sum of the students playing each instrument.
2. A circle graph (or pie chart) represents 100% of the data, which corresponds to a full circle of 360 degrees.
3. The central angle for each sector of the circle graph is proportional to the number of students playing that instrument.

STEP 2

First, we need to find the total number of students in the band by adding the number of students playing each instrument.
Total number of students=Number of students playing Drums+Number of students playing Trumpet+Number of students playing Guitar+Number of students playing ViolinTotal\, number\, of\, students = Number\, of\, students\, playing\, Drums + Number\, of\, students\, playing\, Trumpet + Number\, of\, students\, playing\, Guitar + Number\, of\, students\, playing\, Violin

STEP 3

Now, plug in the given values for the number of students playing each instrument to calculate the total number of students.
Total number of students=8+11+9+8Total\, number\, of\, students = 8 + 11 + 9 + 8

STEP 4

Calculate the total number of students in the band.
Total number of students=8+11+9+8=36Total\, number\, of\, students = 8 + 11 + 9 + 8 = 36

STEP 5

Next, we need to find the proportion of the total that the number of students playing Drums represents.
Proportion of Drums=Number of students playing DrumsTotal number of studentsProportion\, of\, Drums = \frac{Number\, of\, students\, playing\, Drums}{Total\, number\, of\, students}

STEP 6

Plug in the values for the number of students playing Drums and the total number of students to calculate the proportion.
Proportion of Drums=836Proportion\, of\, Drums = \frac{8}{36}

STEP 7

Simplify the fraction to find the proportion of the total that the number of students playing Drums represents.
Proportion of Drums=836=29Proportion\, of\, Drums = \frac{8}{36} = \frac{2}{9}

STEP 8

To find the central angle for the sector representing Drums, we multiply the proportion of Drums by the total degrees in a circle.
Central angle for Drums=Proportion of Drums×Total degrees in a circleCentral\, angle\, for\, Drums = Proportion\, of\, Drums \times Total\, degrees\, in\, a\, circle

STEP 9

Now, plug in the proportion of Drums and the total degrees in a circle (360 degrees) to calculate the central angle for Drums.
Central angle for Drums=29×360 degreesCentral\, angle\, for\, Drums = \frac{2}{9} \times 360\, degrees

STEP 10

Calculate the central angle for the sector representing Drums.
Central angle for Drums=29×360 degrees=80 degreesCentral\, angle\, for\, Drums = \frac{2}{9} \times 360\, degrees = 80\, degrees
The central angle for the sector representing Drums is 80 degrees.

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