Question

question 4 of 10
in a circle of radius 25 inches, a central angle of 35° will intersect the circle
forming an arc of length ____.

a. 15.27 inches
b. 15.27 feet
c. 875 inches
d. 1.17 feet

Explanation:

Step1: Recall the 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 \( s=\frac{\theta}{360^\circ}\times2\pi r \). Here, \( r = 25 \) inches and \( \theta=35^\circ \).

Step2: Substitute the values into the formula

Substitute \( r = 25 \) and \( \theta = 35^\circ \) into the formula:
\[

$$\begin{align*} s&=\frac{35^\circ}{360^\circ}\times2\times\pi\times25\\ &=\frac{35}{360}\times50\pi\\ &=\frac{35\times50\pi}{360}\\ &=\frac{1750\pi}{360}\\ &\approx\frac{1750\times3.1416}{360}\\ &\approx\frac{5497.8}{360}\\ &\approx15.27 \end{align*}$$

\]
The units are inches since the radius was given in inches.

Answer:

A. 15.27 inches