For the problem below, θ is a central angle in a circle of radius r . Find the length of arc s cut off by θ . θ = 25°, r = 3 mm.

A)s = 1.31 mm
B)s = 1.11 mm
C)s = 2 mm
D)s = 5 mm
E)s = 1.21 mm

Question

For the problem below, θ  is a central angle in a circle of radius r . Find the length of arc s cut off by θ . θ = 25°, r = 3  mm.
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A)s = 1.31 mm
B)s = 1.11 mm
C)s = 2 mm
D)s = 5 mm
E)s = 1.21 mm

Quizplus · Accepted Answer

The length of an arc, $s$, in a circle is given by the formula $s = r\theta$ when $\theta$ is in radians. To use this formula with degrees, we first convert $\theta$ from degrees to radians: $\theta = 25^\circ = \frac{25\pi}{180}$ radians. Then, $s = 3 \times \frac{25\pi}{180} = \frac{75\pi}{180} = \frac{5\pi}{12}$ mm. Numerically, this is approximately $s = 1.31$ mm.

For the Problem Below, θ Is a Central Angle in a Circle