Question

Find the length of an arc of a circle subtended by an angle of 108 with a radius of 48 inches. also find the area of the secotr of the circle cut by the same angle

Answer 1

arclength (s) = θ · radius(r) ; where "θ" is in radians

`(\pi)/(180)` =
`(θ)/(108)`

108 π = 180(θ)

`(108)/(180)`π = θ

`(3)/(5)`π = θ

s = θ · r

=
`(3)/(5)`π · 48

=
`(144)/(5)`π

Answer:
`(144)/(5)`π inches

Area of circle = π · r²

Area of sector =
`(108)/(360)` · π · (48)²

=
`(3)/(10)` · π · 2304

=
`(6912)/(10)` · π

Answer: 691.2π in²