Question

A circle has a radius of 5.4 m. What is the exact length of an arc formed by a central angle measuring 60°? Please explain the math!

Answer 1

Answer:

The length of an arc(l) is given by:

$l = r \theta$

where,

r is the radius of the circle

$\theta$ is the angle in radian.

As per the statement:

A circle has a radius of 5.4 m.

⇒$r = 5.4 m$

It is also given that: a central angle measuring 60°

⇒$\theta = 60^{\circ}$

Use conversion:

1 degree = 0.0174533 radian

then;

60 degree =1.0472 radian

Substitute the given values we have;

$l = 5.4 \cdot 1.0472 = 5.65488 m$

Therefore, the exact length of an arc is, 5.65488 m

Answer 2

If radius = 5.4 then circle circumference = 5.4*2*PI = 33.9292

60 degrees is one sixth of a circle so the arc length = 33.9292 / 6

So the arc length = 5.6549 m