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

$\frac{\pi}{180}$ =    $\frac{θ}{108}$

108 π = 180(θ)

$\frac{108}{180}$π = θ

$\frac{3}{5}$π = θ

s = θ · r

  = $\frac{3}{5}$π · 48

  = $\frac{144}{5}$π

Answer: $\frac{144}{5}$π inches

Area of circle = π · r²

Area of sector = $\frac{108}{360}$ · π · (48)²      

                        =  $\frac{3}{10}$ · π · 2304

                        = $\frac{6912}{10}$ · π

Answer: 691.2π in²