Question

What is the arc length of arc CD in the circle below?

Answer 1

Answer:

Option D is correct

the arc length of arc CD in the circle is, 11.780 feet

Step-by-step explanation:

Formula for arc length is given by:

$l =r \theta$            ....[1]

where

r is the radius and $\theta$ is in radian.

From the figure we have;

r = 15 ft

$\theta = 45^{\circ}$

To convert degree in radian:

1 degree = 0.0174533 radian

then;

45 degree = 0.7853985 radian.

Substitute these values in [1] we have;

$l = 3.14 \cdot 0.7853985 = 11.7809775$

Therefore,  the arc length of arc CD in the circle is, 11.780 feet

Answer 2

The arc will be a proportion of the circumference.

The circumference is 2πr = 6.28(15 ft) = 94.2 ft

The proportion is 45/360

Then the arc is (45/360)*94.2 ft = 11.78 ft