Question

What is the arc length of a circle that has a 7-centimeter radius and a central angle that is 40 degrees? use 3.14 for π and round your answer to the nearest hundredth. 0.70 centimeter 4.88 centimeters 7.40 centimeters 280.01 centimeters?

Answer 1

Arc Length of a sector with 40° as central angle= 2πR¶/ 360
= 2*3.14*7*40/360
= 4.8 cm
= 5 cm(approx)

Answer 2

The arc length is 4.88 centimeters.

Explanation:

Since, the arc length of a circle formula is,

`l = r* \theta`

Where, r is the radius of the circle,

`\theta` is the central angle ( in radians ) by the arc,

Given,

`r=7\text{ cm}`

`\theta = 40^(\circ)=(\pi)/(180)* 40 = (3.14)/(180)* 40=(125.6)/(180)\text{ radians}`

`\because \pi\text{ radians}=180\text{ degrees}`

Hence, the arc length would be,

`l=7* (125.6)/(180)=(879.2)/(180)=4.8844\approx 4.88\text{ cm}`