Question

A sector has an area of 40cmsquared, and an angle of 30 degrees. The arc length of the sector, to 2 decimal points is:
a)1.64cm
b)2.66cm
c)4.83cm
d)6.47cm
e)12.36cm

Answer 1

\[r^2/2*\theta \] is the area of a sector formula

Answer 2

arc length formula is \[2\pi*r*\theta\]

Answer 3

d)6.47cm
30/360 = 40(/pi r^2) --> this gives the portion or the circle's area covered by the sector
1/12 = 40/(3.14 r^2)
3.14 r^2 = 12*40
r^2 = 480/3.14
r ^2 = 152.866
r = 12.36
--------------
30/360 = AL/[2 pi (12.36)] --> this gives the portion of the circumference length covered by the arc where AL represents the length of the arc
1/12 = AL/77.645
AL = 6.470

Answer 4

@Directrix: Thank you! But I don't understand what you did at the end

Answer 5

@Genuine --> Do you follow how I got the radius of the circle?

Answer 6

Yes!

Answer 7

When you find arc length, what formula do you use?

Answer 8

θ/360 x circumference

Answer 9

@Directrix: But what does AL mean?

Answer 10

AL is arc length as in Arc Length = θ/360 x circumference
AL = 30/360 * 2 pi (r) =
AL = 1/12 * 6.28 ( 12.36) = 6.47

Answer 11

OH! Now i understand

Answer 12

@Directrix: I see what I had done wrong before, instead of square rooting 480 to find the radius I just divided the equation...

Thank you so much for helping me (: