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

Question

3 years ago

5

of the circle cut by the same angle

1 answer:

AleksandrR [38] · Answer 1 · 2022-04-22T15:43:22+03:00

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