Question

a. find the length of a 15° arc of a circle whose radius is 4 cm.
b. explain why the arc length in part (a) is longer or shorter in centimeters if the radius had been 7 cm.
c. find the arc length when the radius is increased to 7 cm.

a. the length of the 15° arc is □ cm
(simplify your answer. type an exact answer, using π as needed. use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Recall the arc - length formula

The formula for the arc length \(s\) of a circle is \(s=\frac{\theta}{360}\times2\pi r\), where \(\theta\) is the central angle in degrees and \(r\) is the radius of the circle.

Step2: Substitute the values for part (a)

Given \(\theta = 15^{\circ}\) and \(r = 4\space cm\).

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Answer:

\(\frac{\pi}{3}\)