Question

Find the length of the arc of a circle of radius 5.02 miles subtended by a central angle of π/3 radians. Round your answer to the nearest hundredth.The length of the arc is __ miles.

Answer 1

5.26 miles

Explanation:

Given a circle with radius, r, the length of the arc, s, subtended by an angle θ, (θ in radians) is calculated using the formula:

`s=\theta r`

Given:

• Radius, r = 5.02 miles

,

• The central angle = π/3 radians

Then:

`s=(\pi)/(3)*5.02=5.26\text{ miles}`

The length of the arc is 5.26 miles (rounded to the nearest hundredth).