Question

In a circle with a radius of 12.6 ft, an arc is intercepted by a central angle of 2 radians

Answer 1

Question:

In a circle with a radius of 12.6 ft, an arc is intercepted by a central angle of 2π/7 radians.

What is the arc length?

Use 3.14 for π and round your final answer to the nearest hundredth.

Enter your answer as a decimal in the box.

Answer:

Arc length is 11.30 feet

Solution:

Given that,

Radius of circle = 12.6 feet

Central angle = $\frac{2 \pi }{7}$ radians

To find: Arc length

The arc length of a circle of radius "r" when central angle given in radians is:

$s = r \times \theta$

Where,

s is the arc length

r is the radius

$\theta$ is the central angle in radians

Substituting the values we get,

$s = 12.6 \times \frac{2 \times \pi }{7}\\\\s = 12.6 \times \frac{2 \times 3.14 }{7}\\\\x = 11.304 \approx 11.30$

Thus, arc length is 11.30 feet