Area

[strange crystal]

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[junior plover]

Where do you get stuck?

Do you just not know where to start @strange crystal

[strange crystal]

Yes I don't know where to begin

[junior plover]

Do you know the formula for the sector of a circle?

[strange crystal]

no

Wait, is it theta/360 x 2pir?

[junior plover]

Yeah exactly

And this should make sense because

Well

Wait sorry

$$\frac{\theta}{360^o} \times \pi r^2$$

[low sky]

PapaBread

[junior plover]

Thats it I misread your formula

[strange crystal]

Oh ok

[junior plover]

And this should make intuitive sense because like

[strange crystal]

What is the formula that I typed? Is it for an arc?

[junior plover]

Yeah the arclength of a sector

[strange crystal]

Ok

[junior plover]

All of these formulas work on the same basic principle though

The fraction of a whole circle a sector takes up * whatever

So like if the angle was 180° then obviously that would be half of the circle and therefore half the area

[strange crystal]

Why would it be half of the circle?

[junior plover]

Or in your case if the angle is 33° then that makes up 33°/360°=9.167% about of the circle

[junior plover]

Like imagine if you had 180° of a pizza

It would just be half of the pizza

Half of the amount of pizza (area), half of the length of the crust (arclength) etc

[strange crystal]

Oh right

[junior plover]

So like if you break up the formula into two parts

[strange crystal]

What is the radius?

[junior plover]

So in the first one

Youre looking at sector OAB right

[strange crystal]

Yes

[junior plover]

So this little thing

If you imagine the full circle that sector would make if you extende out whats the radius of that

Or if you just look at the little bit of the circle you can see

[strange crystal]

12?

[junior plover]

No its 55 cm

[strange crystal]

I thought you meant the radius of the unshaded part

[junior plover]

Oh I see where you were going with that

Yeah no sorry I was just asking for the radius of the circle that makes up sector OAB

Since thats what part a wants

[strange crystal]

Ok, but the radius is half but isn't that part slanted?

The slant height would be shorter than the perpendicular height

[junior plover]

Well this is a circle

So the distance from the center to any point on the circle is the same

Which is the definition of hte radius

[strange crystal]

I see

[junior plover]

So now try applying the formula to all of the variables you have

[strange crystal]

So 33/360 x 3.14 x 55 x 55?

[junior plover]

Mhm

[strange crystal]

I got a decimal, 870.6958333

Should I round up?

[junior plover]

It depends what your teacher wants

Youre gonna want to save this answer for later so for calculating purposes I wouldnt round it

[strange crystal]

Ok

[junior plover]

Alright so now for part b

Do you kinda have an idea of what you need to do for this one?

[strange crystal]

Arc? 😄

It says area

The length for the two sides would be 12

But whay would be the width?

Do we use theta/360 x 2pir?

[junior plover]

Well its not a rectangle

Youd need a special formula to find the area using the length and width of it

Theres an easier way using two sector area calculations

[strange crystal]

What do you use the formula of the arc for?

[junior plover]

Imagine you had like

Im gonna keep going with the pizza analogy

If you had a big piece of pizza and you took a perfectly circular bite out of it

So the white is the pizza and the red is the bite

[strange crystal]

Yes

[junior plover]

If the pizza originally had an area of 30 cm^2 and the bite had an area of 20 cm^2 how much pizza would be left in that outer segment

The crust

[strange crystal]

10cm²

right?

[junior plover]

Yeah

So now you can do the same thing here

You have all the tools you need to find the original area of the pizza and the "bite"

[strange crystal]

But we didn't find D or C before

We only have the bite

[junior plover]

Yeah so now you just need to calculate one more thing

Then you're set

The area of segment OCD

[strange crystal]

😎 I see

33/360 x 3.14 x 67 x 67

[junior plover]

Yes

[strange crystal]

1292.083833

Now we just subject this with the previous value?

[junior plover]

Yeah

[strange crystal]

I see, so that is why we could not round up

[junior plover]

Indeed

And also if you like fancy formulas you can also kinda condense all of this

Cause we have

$\frac{\theta}{360^o} \pi r_2^2 - \frac{\theta}{360^o} \pi r_1^2$

[low sky]

PapaBread

[junior plover]

Then you can factor out all of that extra nasty stuff and youre left with just

$\frac{\theta}{360^o} \pi (r_2^2 - r_1^2)$

[low sky]

PapaBread

[strange crystal]

Thats good, I can verify!

What is this formula for?

[junior plover]

The area of a segment between two radii

Just like ABCD

Like a watermelon rind

[strange crystal]

Oh ok

[junior plover]

So anything like this

You just use the segment formula but instead of r you use r2-r1

But you dont really need to remember any of this its just a shortcut if you want

You can figure it out just using the one theta/360° * pi r^2 too

[strange crystal]

How do I find ab?

Paternal loaf?

@junior plover

[junior plover]

Why do you need AB?

[strange crystal]

It says to find the length of it for C

[junior plover]

Oh

True true

I thought you were still on part b

Do you remember that formula you said earlier

[strange crystal]

Yes theta/360 x 2pir

33/360 x 2 x 3.14 x 55?

[junior plover]

Ye

Thats it

[strange crystal]

1741.391667

[junior plover]

,calc 33/360 * 2 * pi * 55

[low sky]

Result:

31.677725923697

[junior plover]

Did you accidentally do it squared or sm?

[strange crystal]

I'll check

I used my phone calculator and I got your answer, but my scientific calculator is giving me a different one

Which means my previous answers could be wrong as well

[junior plover]

,calc 33/360 * pi * (67^2 - 55^2)

[low sky]

Result:

421.60173411175

[strange crystal]

Oh, I did it in the calculator and I got your answer, I must've done something wrong

[junior plover]

Hmmm

Are you getting the order of operations wrong or sm

[strange crystal]

Maybe, ill check

It is just my calculator

[junior plover]

Your answer is 3/360 * pi * 55^2 * 2 or something

[strange crystal]

Yes, I'll do your answer since I got the same answer on my phone calculator

[junior plover]

Alright

You might wanna figure out whats wrong with your scientific calculator though

[strange crystal]

It is complicated to use in itself, before I get a whole number it first puts it in a fraction, then I have to press two other buttons to revert it back to a whole number, every single time

It also has other mathematical operations like statistics, distribution, ratio, spreadsheet etc I hate it

Oh, do you know how to get D? @junior plover

[junior plover]

Wdym D

[strange crystal]

It says to calculate the radius of the circle formed by the arc AB

[junior plover]

That should just be the same radius as the inner arc right

[strange crystal]

Yes

Oh, so 12?

[junior plover]

I think its 55

[strange crystal]

I'm not sure

@junior plover But thank you for the help! +1 rep ☝️

[half anvil]

@strange crystal has given 1 rep to @junior plover

[junior plover]

Yeah of course

[strange crystal]

@junior plover Hi, do you have time to help me with another question?

[junior plover]

Sure

[strange crystal]

@junior plover

[junior plover]

This is the same thing basically you're just subtracting two areas

[strange crystal]

@junior plover I'm doing it now and just realized I had the radius as 5 for the smaller circle and 10 for the bigger circle, is that right?

[strange crystal]

Also for this, is the area 7x11=77?

[junior plover]

Yes

[junior plover]

No

It's a semicircle and a rectangle

[strange crystal]

@junior plover would I do pir²/4

[junior plover]

That's part of it yes