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11.4: Circumference and Arc Length
Objectives:• Develop and apply the equation for the circumference of a circle• Determine arc length of a circle
Common core standards:• A-SSE-1, G-CO-1, G-C-5, G-MG-1, N-Q-1
A circle is the locus of points in a plane that are a fixed distance from a point called the center of the circle. A circle is named by the symbol and its center. A has radius r = AB and diameter d = CD.
Solving for C gives the formulaC = d. Also d = 2r, so C = 2r.
The irrational number is defined as the ratio ofthe circumference C tothe diameter d, or
EXAMPLE 1Find the indicated measures.
The exact circumference of a circle with radius 9 centimeters
The exact radius of a circle with circumference 26 meters
EXAMPLE 2
The dimensions of a car tire are shown at the right. To the nearest foot, how far does the tire travel when it makes 15 revolutions?
Tire Revolutions
GUIDED PRACTICE Find the circumference of a circle with diameter 5 inches.
Find the diameter of a circle with circumference 17 feet.
EXAMPLE 3Find the length of each red arc.
Find the indicated measure.
Circumference C of Z
EXAMPLE 4Find the indicated measure.
m RS
GUIDED PRACTICEFind the indicated measure.
Length of PQ
9 is the diameter
GUIDED PRACTICE
Circumference of N
Find the indicated measure.
GUIDED PRACTICE
Radius of G
Find the indicated measure.