Question

Use the arc length formula and the given information to find r. Show your work for full credit. s = 8.1 ft θ = (3.14/3)rad r = ?

Answer 1

This question is simple I'm a little confused on the specifics so I will try my best to help.

s=θ(r)
arc length = angle x radius
2.46888m(or 8.1 ft) = (π/3) x r

`r = (\pi /3)/2.46888`

`r = .425m`

Answer 2

The length of the radius is 7.74 ft.

Explanation:

It is given that the length of arc is s=8.1 and central angle of arc is
`\theta=(3.14)/(3)` in radian.

The formula for arc length is

`s=r\theta`

Where, s is length of arc, θ is central angle of arc in radian and r is the radius of the circle.

Substitute s=8.1 and
`\theta=(3.14)/(3)` in the above formula.

`8.1=r* (3.14)/(3)`

`8.1=r* 1.0467`

Divide both sides by 1.0467.

`(8.1)/(1.0467)=r`

`7.73860705073=r`

`r\approx 7.74`

Therefore the value of r is 7.74 ft.