Question

A circle has a radius of \blue{3}3start color #6495ed, 3, end color #6495ed. An arc in this circle has a central angle of 60^\circ60 ∘ 60, degrees. What is the length of the arc?

Answer 1

Answer:

The length of the arc is 3.14 units.

Step-by-step explanation:

Given:

Radius of the circle is, $R=3\ units$

Central angle of an arc is, $\theta=60$°

We know that, for a circular arc of radius 'R' and central angle of the arc as $\theta$ radians, the length of the arc is given as:

$L=R\theta$

Here, the central angle is in degrees. So, converting degrees to radians we get:

$\theta=60\times \frac{\pi}{180}\\\theta=\frac{\pi}{3}\ radians$

Plug in 3 for 'R', $\frac{\pi}{3}$ for $\theta$ and solve for 'L'. This gives,

$L=3\times \frac{\pi}{3}\\L=\frac{3\pi}{3}\\L=\pi=3.14\ units$

Therefore, the length of the arc is 3.14 units.

Answer 2

Answer:

3.142units

Step-by-step explanation:

The formula for calculating the length of an arc is as given below;

Length of an arc = theta/369° × 2πr where:

r is the radius of the circle

theta is the central angle

Given the data

r = 3, theta = 60°

Length of an arc = 60/360 × 2π(3)

Length of an arc = 1/6× 6π

Length of an arc = π units

Length of an arc = 3.142units