Question

find the length of the arc, s, on a circle of radius r intercepted by a central angle θ. express the arc length in terms of π. then round your answer to two decimal places.
radius, r = 11 inches; central angle, θ = 35°
s = □ inches
(simplify your answer. type an exact answer in terms of π. use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Recall arc length formula

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

Step2: Substitute values

Given \( r = 11 \) inches and \( \theta=35^{\circ} \), substitute into the formula:
\( s=\frac{35}{360}\times2\pi\times11 \)
Simplify the fraction \( \frac{35}{360}=\frac{7}{72} \), so:
\( s=\frac{7}{72}\times22\pi=\frac{7\times22\pi}{72}=\frac{77\pi}{36} \)
To find the decimal approximation, calculate \( \frac{77\pi}{36}\approx\frac{77\times3.1416}{36}\approx\frac{241.9032}{36}\approx6.72 \) (rounded to two decimal places). But first, the exact answer in terms of \( \pi \) is \( \frac{77\pi}{36} \).

Answer:

The exact arc length in terms of \( \pi \) is \( \frac{77\pi}{36} \) inches (and the approximate value is \( 6.72 \) inches). For the exact answer as required first, the answer is \( \frac{77\pi}{36} \).