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.

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11.4 Circumference and Arc Length

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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 formula C =  d. Also d = 2r, so C = 2r. The irrational number  is defined as the ratio of the circumference C to the diameter d, or

EXAMPLE 1 Find 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 4 Find the indicated measure. m RS

GUIDED PRACTICE Find 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.