Question

find the approximate length of minor arc ab. use 3.14 for pi. round to the nearest hundredth.
57.35 m
6.41 m
12.72 m
43.86 m

Explanation:

Step1: Recall arc length formula

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

Step2: Identify given values

Here, \( \theta = 81^{\circ} \), \( r = 9\space m \), and \( \pi\approx3.14 \).

Step3: Substitute values into formula

First, calculate \( 2\pi r \): \( 2\times3.14\times9 = 56.52\space m \) (this is the circumference of the circle).
Then, find the fraction of the circumference corresponding to the arc: \( \frac{81^{\circ}}{360^{\circ}}\times56.52 \).
Simplify \( \frac{81}{360}=\frac{9}{40} \).
Now, multiply: \( \frac{9}{40}\times56.52 = 9\times1.413 = 12.717\space m \).

Step4: Round to nearest hundredth

Rounding \( 12.717 \) to the nearest hundredth gives \( 12.72\space m \).

Answer:

12.72 m