We know that :
[tex]\bigstar[/tex] Circumference of a Circle is given by : 2πr
This Circumference of the Circle subtends an angle of 360° at the center
Length of the Arc which subtends an angle θ at the center is given by :
[tex]\implies \sf{Length = 2\pi r \bigg(\dfrac{\theta}{360}\bigg)}[/tex]
Given : θ = 110° and Radius (r) = 4 inches
Substituting in the above formula, We get :
[tex]\implies \sf{Length = 2(3.14)(4)\bigg(\dfrac{110}{360}\bigg)}[/tex]
[tex]\implies \sf{Length = 2(3.14)\bigg(\dfrac{11}{9}\bigg)}[/tex]
[tex]\implies \sf{Length = 7.67555}[/tex]
Rounding of to the nearest hundredth, We get :
[tex]\implies \sf{Length = 7.68}[/tex]
