Question

Find the length of an arc of an 8" radius circle if the arc measures 45 degrees. 2pi, 8pi, 16pi

Answer 1

The length of the arc is 2π. Therefore the correct option is 1.

Explanation:

The length of arc is

`l=r\theta` .... (1)

Where, r is the radius of the circle and θ is central angle in radian.

It is given that the radius of the circle is 8 units and the central angle is 45 degrees.

Convert the central angle in radian.

`45* (\pi)/(180)=(\pi)/(4)`

Substitute r=8 and
`\theta=(\pi)/(4)` in equation (1).

`l=8* (\pi)/(4)`

`l=2\pi`

The length of the arc is 2π. Therefore the correct option is 1.

Answer 2

To find the length of the arc, we will use the formula,
arc length = 2πR (C/360)

where,
R is the radius of the arc, which is 8"C is the central angle, which is 45°
pi is approximately equivalent to 3.14


Applying the formula,arc length = 2πR (C/360)
arc length = 2(3.14)R (45°/360)
arc length = (6.28)(8") x (0.125)
arc length = (50.24") (0.125)
arc length = 6.28"

The length of the arc is 6.28". 6.28 is also equivalent to 2π, hence, the answer is 2π.