Question

A carousel horse travels on a circular path with a radius of 15 feet. How many feet does the horse travel over an angle of 2pi/3 radians? Round to the nearest foot.

Answer 1

Answer: 31

Explanation:

I got it right

Answer 2

31 foot

Explanation:

Radius of the circular path = 15 feet

Angle of horse travel on a circular path =
`(2\pi )/(3)` radians = Central Angle

Central angle =
`(2\pi)/(3) * (180)/(\pi)` degrees = 120°

Distance travelled by the carousel horse on the circular path over an angle of
`(2\pi)/(3)` = Arc length

We can use the formula below to calculate arc length;

°
`(Central Angle)/(360) = (Arc length)/(2\pi r)`

`(120)/(360) = (Arc length)/(2\pi* 15)`

Arc length =
`10\pi`

Arc length = 31.4 foot

Arc length (rounded to the nearest foot) = 31 foot