Question

Help!
The area of sector JLK is 3pie inches^2 Find m arc JK
pic attaced

Answer 1

You know the radius of the circle. So you know the total area of the circle. Now you know the area of the shaded area as well, right? So you know what percentage of the circle that section is.

So you know that the length of the arc is a certain percentage of the circumference of the circle.

Now can you do the problem?

Answer 2

Hey heather :) hope I'm not finding this too late. We can absolutely solve this equation using circle equations. I believe we will need the following:
\[A_{circle}=\pi*r^{2}\]
\[S=\frac{\theta (degrees)}{360(degrees)}*2\pi r\]
Where r is our radius, S is our arc length, and theta is our arc angle. The arc length equation actually comes from the equation for the circumference of a circle (C=2pi*r), because an arc is a fraction of a circle

Answer 3

@heather040200 are you following me so far?

Answer 4

im with u so far

Answer 5

cool :) I think the next step would be to move everything in your arc equation to the left side. You think you can do that for me? We can solve this with a little algebra.

Answer 6

*except for r. We want that on the right side

Answer 7

im kinda confused not would it be Aone pie=6^2

Answer 8

or would it be 3pie=6^2

Answer 9

Actually, I think to find your arc's area, you can put the fraction theta/360 in front of the area equation. I can't see the radius in your problem. Would you mind letting me know what it is?

Answer 10

and what is your question referring to?

Answer 11

oh ya sorry its 6

Answer 12

er wait idk do you see the 6 in the proble at all

Answer 13

oh! then we can simplify some stuff!
\[A_{S}=3\pi=\frac{\theta}{360} * \pi * 36\]

Answer 14

If what I wrote above is correct, then you can get your theta and solve for S in the second equation

Answer 15

so far i have 3pie=360*pie+36

Answer 16

and @Rav, if you see any mixups in my steps, feel free to butt in :)

Answer 17

is that right

Answer 18

Area of a circle = pi*r^2
Circumference of a circle = 2pi*r

r = 6
Area = 36pi
Area of shaded area = 3pi = a
a/A = 3/36 = 1/12

Circumference of circle = 2pi*6 = 12pi

Arc length = pi

Answer 19

Ta-daa

Answer 20

no....In the area equation you should be getting 3pi=(theta/360) * pi * 36

Answer 21

So you want theta or you want the length of arc JK?

Answer 22

I wanted to show her how to use theta to get arc length

Answer 23

Why not just get the arc length in 25 seconds like a boss

Answer 24

because I don't know how to do that, and this could be helpful in systems of equations

Answer 25

If she doesn't know how to get the arc length from first principles then using theta is above her level. Math is about building on previous knowledge not about jumping into the hard stuff.

Answer 26

I thought it would be the opposite...

Answer 27

ok so for the area i got 37.69

Answer 28

not in terms of learning

Answer 29

6^2 = 36
Area = pi*r^2 = pi*36 = 36pi

Answer 30

but that I was doing a more step by step way

Answer 31

so take 36 times pi

Answer 32

Area of a circle = pi*r^2
Circumference of a circle = 2pi*r

r = 6
Area = 36pi
Area of shaded area = 3pi
[Shaded area]/[Total area] = 3/36 = 1/12

Circumference of circle = 2pi*6 = 12pi

Arc length = ([shaded area]/[total area]) * circumference

Answer 33

Alright worked it

Answer 34

Imagine if you have a whole cake, and you know how much cake you have. Then you take a slice that is exactly 1/12th of the cake. How much of the cake's circumference is now missing?

Answer 35

i don't really understand what ur asking

Answer 36

like i don't get how to get the answer

Answer 37

so without the full area you can solve the problem like this:

\[A=\theta/360 * \pi 36(inches^2)\]
\[A=3*\pi\]
\[3\pi=\theta/360 * \pi * 36\]
cancel 36 with 360 to get 10
\[3 \pi = \theta/10 *\pi\]
multiply both sides by 10
\[30\pi=\theta \pi\]
cancel out pi
\[\theta= 30 (degrees)\]
S=theta/360 * 2 * pi * 6
plug in your thetat (r is 6)
\[S=30/360 * 2 * \pi * 6\]
\[S=\pi\]

Answer 38

Here we go!

Answer 39

The circumference of a circle is the total distance from a point on the edge of the circle to the same point, by going all the way around. If you take away 1/12 of the total circumference, how much of the circumference is left?

Answer 40

do u want me to solve that @karma

Answer 41

that's solved

Answer 42

xD

Answer 43

look through it and tell me if there's anything that looks confusing :)

Answer 44

oh sorry i didn't see that i thought u were talking me threw without giving me tha e answer

Answer 45

I was going to, but why confuse you when I can give you it and show how?

Answer 46

so the answer i pie?

Answer 47

Area of a circle = pi*r^2
Circumference of a circle = 2pi*r

r = 6
Area = 36pi
Area of shaded area = 3pi = a
a/A = 3/36 = 1/12

Circumference of circle = 2pi*6 = 12pi

Arc length = pi

I GET THE FEELING YOU DIDN'T READ THIS THE FIRST TWO TIMES I WROTE IT

Answer 48

i can read it but i cant understand it/ don't get it! its easyer if thirs numbers pluged in!

Answer 49

yes! the answer is indeed pi, because math teachers are trolls xD in the solution I set JKL=S because you'll learn in trigonometry that S is the letter for arc length.

Answer 50

You should look up the basic formulas regarding circles. It's important to understand how to calculate the area and circumference of a circle using the radius.

Answer 51

let's not all respond at once!

Answer 52

xD

Answer 53

he said, while responding at once

Answer 54

so i put pi for my answer lol just making sure i understand what ur saying @karma

Answer 55

Nothing I say is having any effect. Ciao...

Answer 56

yes, pi inches

Answer 57

Thank you very much for your help

Answer 58

and do you get where I got it?

Answer 59

yes i understand where you got it

Answer 60

But you don't understand circumference?!

Answer 61

cool!

Answer 62

so it's basically just working with two equations that are fractions of your area=pi*r^2 and circumference (think wrapping a piece of tape around a circle once, then measuring its length) = 2*pi*r

Answer 63

ok