Question

What is the central angle of a sector with an arc length of 10 cm in a circle of radius 5 cm?

• A. 6 radians
• B. 3 radians
• C. 2 radians
• D. 4 radians

Answer 1

Answer:

C. 2 radians

We use the arc length formula:

$s = r\theta$
]

Given:

• Arc length (s = 10) cm

• Radius (r = 5) cm

So,

$\theta = \frac{s}{r} = \frac{10}{5} = 2$
$\theta = \frac{10}{5} = 2\ \text{radians}$

Therefore, the central angle is 2 radians.