Circle Gemonrety Math Problem Help??
An indoor track is in the shape of a circle with radius 32 m. Quinn ran 3/4 of the way around the track.
a) What distance did Quinn run?
b) What is the central angle subtended by the path Quinn ran around the track? Explain how you determined the angle.
c) Isha ran a path that subtends a central angle of 200 degrees. What distance did she run?
- ArgentLv 71 year agoFavorite Answer
a) The circumference of a circle is 2πr, so Quinn ran (3/4)(2π)(32 m) = 151 m (rounding to nearest integer).
b) There are 2π radians in a circle. Quinn ran 3/4 of the total arc, so the angle is 3/4 of the total: (3/4)(2π) = 4.7 radians, or 1.5π radians.
c) Use s = rθ, where s is the arc length; r is the radius; and θ is the (central) angle. You have to use radians for this, though, so convert 200° to radians: (200°)(π/180°) = 3.49 radians, or (10/9)π.
s = (32 m)(10π/9) = 112 m (rounding again).