Question

How long is the arc intersected by a central angle of 5pi/3 radians in a circle with a radius of 2 ft? Round your answer to the nearest tenth. Use 3.14 for pi

A. 2.6 ft
B. 7.0 ft
C. 10.5 ft
D. 31.4 ft

Answer 1

Length of an arc of a circle:
L = n / 2π ·2 ·r · π
L = (5π/3 ·2 ·2 ·3.14 ) : 2π = 5/3 · 6.28 = 10.47 ≈ 10.5
Answer: C) 10.5 ft.

Answer 2

C

Explanation:

The arc length formula (in radians) is:

`s=r\theta`

Where,

• 
  `s` is the arc length
• 
  `r` is the radius of the circle
• 
  `\theta` is the angle intercepted by the arc [in radians]

It is given that radius,
`r=2` and angle,
`\theta=(5\pi)/(3)`

Substituting these values in the arc length formula gives us:

`s=(2)((5\pi)/(3))\\s=(10\pi)/(3)`

Using
`\pi` as
`3.14` and rounding to nearest tenth gives us:

`s=((10)(\pi))/(3)\\s=10.5` ft

Correct answer is C.