Question

a circle has a central angle measuring \\(\frac{7\pi}{10}\\) radians that intersects an arc of length 33 cm. what is the length of the radius of the circle? round your answer to the nearest whole cm. use 3.14 for \\(\pi\\).\
\\(\bigcirc\\) 11 cm\
\\(\bigcirc\\) 15 cm\
\\(\bigcirc\\) 22 cm

Explanation:

Step1: Recall arc length formula

The formula for the length of an arc \( s \) when the central angle \( \theta \) is in radians is \( s = r\theta \), where \( r \) is the radius of the circle. We need to solve for \( r \), so we can rearrange the formula to \( r=\frac{s}{\theta} \).

Step2: Substitute the given values

We know that \( s = 33 \) cm and \( \theta=\frac{7\pi}{10} \) radians. First, we calculate the value of \( \theta \) using \( \pi = 3.14 \). So, \( \theta=\frac{7\times3.14}{10}=\frac{21.98}{10} = 2.198 \) radians.

Step3: Calculate the radius

Now, substitute \( s = 33 \) and \( \theta = 2.198 \) into the formula \( r=\frac{s}{\theta} \). So, \( r=\frac{33}{2.198}\approx15 \) cm (rounded to the nearest whole number).

Answer:

15 cm