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

Answer:

C

Step-by-step 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, $\theta=\frac{5\pi}{3}$

Substituting these values in the arc length formula gives us:

$s=(2)(\frac{5\pi}{3})\\s=\frac{10\pi}{3}$

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

$s=\frac{(10)(\pi)}{3}\\s=10.5$  ft

Correct answer is C.