Things You'll Need:
- pencil
- paper
- scientific calculator
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Step 1
This graphic of a pizza is a representation of a circle subtended by a central angle...
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Step 2
The RED LINE represents the ARC LENGTH, denoted by the letter 's'...
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Step 3
The BLACK LINES represent the RADIUS, denoted by the letter 'r'...
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Step 4
The GREEN LINE represents the DEGREE MEASURE OF THE CENTRAL ANGLE, denoted by the Greek letter theta...
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Step 5
The BLUE LINE represents the circle's CIRCUMFERENCE, denoted by the letter 'C'
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Step 6
The EQUATION for calculating the ARC ANGLE RELATIONSHIP is theta/360° = s/C = s/2πr
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Step 7
By knowing any two of the three quantities: s, C, or theta, we can calculate the third using basic algebra.
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Step 8
EXAMPLE PROBLEM: Suppose you're asked to calculate the circumference of a pizza. C = ?; s = 4in; theta = 90°
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Step 9
Substitute the values into the arc angle relationship formula... EXAMPLE: (90°)/(360°) = 4/C
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Step 10
It is easier to isolate C if it is in the numerator, so take the reciprocal of both sides (flip the numerator *top* with the denominator *bottom*)... EXAMPLE: (360°)/(90°) = C/4
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Step 11
Multiply both sides by 4, and solve for C... EXAMPLE: (4)(360°)/(90°) = C/4(4); C = (4) * (360°)/(90°); C = 16in
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Step 12
EXAMPLE PROBLEM #2: Suppose you're asked to calculate the arc length of a slice of pizza. theta = 30°; r = 6in; s = ?
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Step 13
Substitute the values into the arc angle relationship formula... EXAMPLE: (30°)/(360°) = s/2π6
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Step 14
Multiply both sides by (2π6), and solve for s... EXAMPLE: (2π6) * (30°)/(360°) = s/2π6 * (2π6)
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Step 15
EXAMPLE: (2π6) (30°)/(360°) = s; s = 3.14in










