Answer:
The length of the arc is
![S =75 . 4 \ m](https://img.qammunity.org/2021/formulas/mathematics/college/aj9too359sc2qwronu7uivu5zidfbyqrht.png)
Explanation:
From the question we are told that
The angle of the quadrant is
![\theta = 90 ^o](https://img.qammunity.org/2021/formulas/mathematics/college/5yxaivxtpttsb8q570mhpydqmyxlnc1rri.png)
The radius of the circle is r =4 m
The angle of the arc is mathematically represented as
![z = 360 - 90 = 270 ^o](https://img.qammunity.org/2021/formulas/mathematics/college/f3cwnbhadr3ybf7174m8s3zqndj0l3ll9k.png)
The length of the arc is mathematically represented as
![S = 2 \pi r [(z)/(360) ]](https://img.qammunity.org/2021/formulas/mathematics/college/cb7f0ropjtl89h7u6db497ijhfgemfo2ic.png)
substituting values
'
![S = 2*(3.142) * 4 [(270)/(360) ]](https://img.qammunity.org/2021/formulas/mathematics/college/cnl0wqv7drsdwi5u1s6h0hc9e0bmgay73x.png)
![S =75 . 4 \ m](https://img.qammunity.org/2021/formulas/mathematics/college/aj9too359sc2qwronu7uivu5zidfbyqrht.png)