Question

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

3.14 feet
4.88 feet
6.98 feet
11.78 feet

Answer 1

Option D is correct

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

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