Question

The sector has an area of 3 pi inches squared and a radius of 6 in. How many inches long is the arc for this sector? Use 3.14 for Pi and round to the nearest hundredth.

A sector with a radius of 6 inches and area of 3 pi inches squared.

Recall that Area of a sector = StartFraction n degrees over 360 degrees EndFraction (pi) (r squared) and StartFraction Arc length over Circumference EndFraction = StartFraction n degrees over 360 degrees EndFraction.
3.14
6.28
12.56
18.84

Answer 1

Answer: 6.28 inches.

Step-by-step explanation:

Formula :

i) Area of sector : $A=\dfrac{x}{360}\times\pi r^2,$, where x = central angle and r is radius

ii) Length of arc : $l=\dfrac{x}{360}\times2\pi r$

Given , r= 6 in.

A = $3\pi$ inches

Put these values in (i) , we get

$3\pi =\dfrac{x}{360}\times\pi (3)^2\\\\\Rightarrow\ 1=\dfrac{x}{120}\\\\\Rightarrow\ x=120^{\circ}$

Now , put values of x and r in (ii) , we get

$l=\dfrac{120}{360}\times2\pi(3)\\\\\Rightarrow\ l=2\pi = 2(3.14)=6.28\text{ inches}$

Hence, the length of the arc is 6.28 inches.

Answer 2

Answer:

6.28

Step-by-step explanation:

Edge 2021