Question

A sector of a circle has a central angle of 135 degrees. Find the area of the sector if the radius of the circle is 11 cm.

Answer 1

\[\frac{x}{360} = \frac{y}{\pi r^2}\]

x = measure of sector = 135
y = area of sector

Answer 2

\[135/360 * 11^2\pi \]

Answer 3

because the area of the circle is pir^2

Answer 4

@muiklover317, what you posted alone doesn't really mean much. It's important to show the ratios of proportionality involved in developing the formula.

Answer 5

you don't necessarily need the proportion.

Answer 6

that's the harder and more complicated way to see this problem.

Answer 7

since it's 360 in circle,

Answer 8

Actually it's easier and simpler.

Answer 9

nope.

Answer 10

it's different for everyone

Answer 11

you can't say this is easier and that is harder. it depends on a person.

Answer 12

that's your way and this is my way.

Answer 13

jhalt is one that will choose the better way for him to solve.

Answer 14

It's the same thing if you think about it. If we use your method, we'll have to remember different formulas for different things. If you use my formula, then you just remember the ratio of proportionality.

Answer 15

it's not the formula and you don't need to memorize it. It's logical. You already know the area and circumference of the circle right?

Answer 16

and you already know that it's gonna be 360 degrees

Answer 17

for me, it's confusing to set the proportion cuz you can easily mess up with the order.

Answer 18

No you can't.

Answer 19

45.375 pi is the answer?

Answer 20

I didn't get that @jhalt

Answer 21

135 times pi times 121/360 = y

Answer 22

@Hero Like I told you, that's YOUR way to solve it. Why do you even need to argue about this?

Answer 23

oh nono @jhalt

Answer 24

you see how 135 is the angle right?

Answer 25

so you have to write (or combine) them together like this: 135/360 times 121pi

Answer 26

cuz 121 is the area of the circle.

Answer 27

Actually @jhalt has it

Answer 28

so isn't it then 16335pi/360?

Answer 29

Simplify that

Answer 30

yeah

Answer 31

it's around 142.55

Answer 32

45.375 pi

Answer 33

thanks for the help guys.

Answer 34

I don't want to cause a dispute so I will not award the best response. Both methods were helpful and I appreciate them

Answer 35

no prob :)

Answer 36

oh you left the pi out okay

Answer 37

The only thing is...@jhalt when you setup the proportion, what you want to do is simplify the fraction when possible. So if you set up this:

\[\frac{135}{360} = \frac{y}{\pi r^2}\]

Answer 38

Simplify the fraction on the left side first before isolating y

Answer 39

ok so its smaller and easier right? But you don't have to correct?

Answer 40

It simplifies to 3/8:

\[\frac{3}{8} = \frac{y}{\pi r^2}\]

Answer 41

ok

Answer 42

thanks

Answer 43

Both methods help

Answer 44

@musiklover317, what if you were given the area of the sector but had to find the angle. Then what would you do?

Answer 45

give me an example question

Answer 46

The area of a sector of the circle is 10. The radius is 5. Find the angle of the sector.

Answer 47

@musiklover317

Answer 48

you don't have pi>?

Answer 49

whateve

Answer 50

It is exactly as you see it.

Answer 51

okay

Answer 52

x = 144

Answer 53

that's the answer okay?

Answer 54

Is that supposed to be your answer to the question?

Answer 55

yeah i got that

Answer 56

That's not correct.

Answer 57

i left out the pi

Answer 58

look.

Answer 59

x/360*25=10

Answer 60

Bro, you don't know how to solve it.

Answer 61

It's still a circle bro.

Answer 62

then show it to me ha

Answer 63

it's the area

Answer 64

Just because I didn't include pi in my question doesn't mean you remove pi from the formula.

Answer 65

oh then you'll have to divide by pi

Answer 66

simple like that.

Answer 67

Okay bro. You got it. But next time, don't remove pi from the formula just because a question doesn't have pi in it.

Answer 68

Suppose you were given the angle of a sector and the area of a sector, but had to find the radius of the circle. Then what would you do?

Answer 69

@musiklover317

Answer 70

Suppose the angle is 216 degrees and the area of a sector is 15pi. What's the radius of the circle?