How to Find the Area of a Sector | Maths GCSE
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- เผยแพร่เมื่อ 6 ก.ย. 2024
- This short explains how to find the area of a sector for Maths GCSE.
Here are the key points to remember:
- First, find the area of the full circle: pi x radius^2
- Then find the fraction of the circle taken up by the sector.
- Calculate pi x raduis^2 x fraction to get the area of the sector!
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You did in 1 minute what my teacher couldn’t do in 2 days
I like how everyone in the comments are people who genuinely wanna learn this stuff but I’m here because my mean maths teacher is giving us a test tmr bc she doesn’t like me and my notebook isn’t written to date 🙃 I love maths honestly- but my teacher is making me slowly but surely strive towards hating it
Soooooo,
Do ya still like maths?
@@mashrafusi like maths
@@chandrakalachan6592 good 😊 proud of u
Don't let a Maths teacher dictate your future remember that
@@apsingh1792 thanks man, this year I actually have a pretty good teacher and either way, math is fun to me now
1/2(angle*radius²) = area of sector
*In radians
Facts
When teaching mate and geometry, try to use ROUND FRIENDLY NUMBERS.
70° is not round and not friendly.
The students can understand 60° much easier, as ⅙ of the circle.
Anyway, beside the weird 70°, good and clear explanation. 👍
Math teacher.
Yeah, I wondered why he'd chosen 70°, as that gives an exact area of 112π/9. Not the friendliest answer.
Tamir don't make excuses. Admit you are an asshole
Interesting and simple method. Here's how I solved it:
Area of a sector formed by an arc= length of arc * radius/2
Length of arc = radius * angle at the centre
angle needs to be in radian for the above formulae, so converting the angle to radian and substituting the relevant values, you end up with the same expression -
(70*π*8^2)/360
It’s something we learn during high school too
Not me. This was something I simply googled. Maybe you were just sitting on your fat, useless body, waiting for school, but others have to start quicker.
@@Sh4dowbanned no need to be so rude though, gosh...😮💨
@@Sh4dowbannedthat's rude and arrogant. You need to change some elements of your behaviour. Wish you a good day and life :)
@@KoczulMoczul mike is just the typical male teen who tries to make himself look cool online by being toxic but in reality he is just not.
@@mathguy3451 you need to have it in the back of your mind that since you are not that person then there is a good chance you don't know what influenced that person to behave this way. Such a person also needs support. Cheers :)
Can only be properly solved by eating pizza and measuring the expansion of your belly.
Bro lifesaver 💯
lightsaber
Do you know what seems odd to me? Numbers that aren’t divisible by two.
the only good math joke ive ever heard. Well done!
For anyone wondering what is the number for pi it's 3.14
3.141592653
Great explanation 😂🎉
Short and sweet
Clear explanation!
Simple 22/7×8×8 (area of circle)
Then (area÷360) × 70 (area of sector)
Use an angle selector formula, 1/2 (theta r^2)
I really wish the TH-cam algorithm blessed me with this video 2 days ago instead of now, this literally popped up on my exam yesterday.
Sadly I can't use a calculator in math p1 during the exam cause we are not allowed 😢
That was way easier than i thought lol
Thank you
You're welcome!
or, you can use radiants to express an Angle...
the sector area is half the angle times r squared if the angle is expressed in radiants
Yep that works too!
Don't know how this works
@@je6845it's just class 11 mathematics
I love ur explanation
Keep it up
1/2(angel*radius ²)=area of sector
39m^2 .and the formula is teta\360*πr^2
this is so simple i looked threw many sources and they were too confusing
Beautifully done
Thank you!
I’m so thankful that I could still figure this out on my own… 😊
you need to be my teacher
Thanks
angle of sector ÷ 360 (total angle of a circle) × 𝝅r2
A better way to write it would be 12 and 4/9 pi
That works too!
You can't express a mixed fraction and then just multiply by variable or symbolized constant thats just janky looking. It looks like your saying 12 + (4/9)pi. You would have to write it as "improper", or if you were in my class I would give you credit if you put the mixed fraction in parentheses.
Thankyou very helpful!
You're welcome!
I understand this.
Good video well done sir
Thanks!
Now teach me how to find the area of a sector of an eclipse
Use calculus.
Well, if it is a total eclipse, the area is zero. Unless you meant "ellipse."
Think of the ellipse as a vertically squished circle; any area in the ellipse is less than the corresponding area in the circle by the factor you squished it by. Now it's just a matter of finding the corresponding sector in the circle which you can do with some trig.
Ask Kepler. He'll know.
Thanks sir 👍
this is lubbly jubbly tysm :D
Thank you studying for union test haven’t done math in awhile an watching every formula video
Thank you very much 👍😊
You're welcome 😊
The ans is 39.11cm^2
awesome, good reminder
352/9
Correct me if I’m wrong, but didn’t you multiply using the diameter? Wouldn’t it be 70/360 * (pi)(4^2) instead of 70/360 * (pi)(8^2)? I’m having trouble figuring out why 8 is the diameter instead of 4.
The sides of a sector are the radius of the circle, not diameter
if you complete the circle, you can clearly see that 8cm is the radius.
Distance from center of the circle to a point on the circle is the radius.
Hello can u pls explain how did this guy get 39 for the answer..
And also 8sq =64 rite so nothing became of that in this equation
@@draymondgreen7606yes, 8² is 64. 64π is around 201 but you need to multiply that to 70/360 which reduces it to 39.
Like your methodology
I think we could take the double integral of one with respect to theta and r…
What about the SECTOR of a ECLIPSE(having different radius,)We can get different anwers man, I mean what about the length of the line touching 7
That should measure different fkr eclipse
Can someone please help me
I have a sector like 1 side is 6 u and other is 4 u and the line segment of 6 u and 4 u intersect at 90°
Help?
I think you mean an ellipse, not an eclipse. An ellipse is an elongated circle, an eclipse is an astronomical event.
Anyway, to find the area of a sector of an ellipse, you need to do a polar coordinate integral. Just like a regular integral, except instead of slicing the function's graph like bread, we're slicing it like a pizza.
Assign r to be the radial distance from the origin, and θ to be the CCW angle in radians, from the +x axis, as is convention. Any given infinitesimal pizza slice will have the area of 1/2*r^2*dθ, where dθ means infinitesimal change in θ.
An ellipse with semimajor and semiminor axes of a and b respectively, in polar coordinates is given by:
r = sqrt(a^2*cos(θ)^2 + b^2*sin(θ)^2)
Thus r^2 = a^2*cos(θ)^2 + b^2*sin(θ)^2
Integrate relative to θ:
cos(θ)^2 = 1/2*(1 + cos(2*θ))
sin(θ)^2 = 1/2*(1 - cos(2*θ))
integral cos(θ)^2 dθ = 1/2*θ + 1/4*sin(2*θ)
integral sin(θ)^2 dθ = 1/2*θ - 1/4*sin(2*θ)
integral 1/2*r^2 dθ =
a^2*(θ/4 + 1/8 sin(2*θ)) + b^2*(θ/4 - 1/8*sin(2*θ)) + C
Evaluate across the angles or interest. Suppose we want to make a 45 degree (i.e. pi/4 radian) elliptical sector, starting on the x-axis. Evaluate from 0 to pi/4:
a^2*(pi/16 + 1/8 sin(2*pi/4)) + b^2*(pi/16 - 1/8*sin(2*pi/4))
Simplify, and we have our result:
a^2*(pi/16 + 1/8) + b^2*(pi/16 - 1/8)
Easy when you know how. Thanks for this.
Our teacher ain’t letting us calculators tho
U don’t need a calculator just leave it in terms of pi
For example if we had an angle of 90/360 and a radius of 10 we would do pi x r^2 which is pi x 10^2 which is 100 pi, since the angle is 90 we times this with 90/360 which gives us 25 pi as the answer and since we don’t have a calculator we just leave it in terms of pi
So we divide 70 / 360 then multiple by 🥧 ?
That's right!
Show more videos of areas 🙏🙏
For who didn't know how to find that area: You don't need to watch this video. All you need a new mind😂
🎉112 pi/9sq cm
Or just convert degrees to radians
How do you find the angle of the circle slice if it is not given and you only have the radius?
You can't.
@@nilsalmgren4492 Is it possible to measure the angle somehow in a real world situation?
@@afifkhaja You can always use a protractor to measure the angle. You cannot know the angle by simply knowing the radius.
Please, explain how to find, in this same sector, the length of the curved line? Would using the definition of Pi and the angle of the sector do?
The arc length of the sector is fairly easy to calculate if you remember how to find the circumference of a circle, which is the diameter multiplied by pi. In this case, we have the radius, 8cm, so we know that the diameter is twice the radius, or 16cm. The circumference would be 16pi.
From there, the arc length of the sector is the circumference of the circle multiplied by the ratio of the sector‘s angle to a full circle. This is similar to finding the area of the sector, which is the area of the circle multiplied by the ratio of the sector‘s angle to the full circle. Thus, the arc length would be (70/360)*16pi, or approximately 9.77384 cm. This is basically saying „if one degree of this circle equates to a length of 16pi/360 around the circumference, what is this length 70 times?“ (16pi/360)*70).
@@isaacbruce6652 Thank you for your elaborate, clear though a bit lengthy response.
Now, in real life one often encounter curves that are not circular, for example, motorways. In elementary geometry, the ellipse, the parabola, the hipérbola... how does one calculate the arc length of different sections in any of these curves, say the ellipse?
Measuring straight lines you use a tape measure between two points, you're done!
Say, garden landscaping: Most likely you plan for curves in your garden which are not a section of a circumference. How to determine their length and therefore the exact quantity of material you need for building them? I am suspecting one needs basic calculus for this.
What if the Angle value is unknown ?
You would have to know the arc length of the sector in order to estimate the angle. If the arc length is equal to (theta/360)*2pi*radius, then you can solve for theta and see that it‘s equal to (arclength*360)/(2pi*radius). In this case, if we had 8cm as the radius and 9.77384 cm as the arc length, then (9.77384*360)/(16pi) would yield approximately 69.9999727, or around 70 degrees. Your precision will be dependent on how the arc length is given.
Wonderful
Very easy
Thanks a lot 😊
Very nice
How to turn a square into a circle by multiplying it with pi?
Sorry what-
I have learnt in class 10th
64pi.(7/36)
Correct.
My final exam is 40/40 thank you
Thanks, realmente Nice..., i Love that
It seemed obvious.
Good
thx bro
Brilliant 🙂
ay I managed to guess this :D
With all the respect, this is low lever geometry in Greece, and maybe to other countries too. Nice video though
Nice
Thanks!
how do you do it as an exact value?
112π/9
What a magic😁😁
My teacher said that the pie is 3.1416 😮😮😮😮😮😮😮😮😮😮
Can't you do π8^2 / 4 ?
Well, that would only work if the angle was 90°
who needs calculator for that laughs in being asian
Hello can u explain how this guy got the answer of 39.
And isnt 8square =64
Bcuz 64×3.14×70/360=39.07(5)
And if you wanted to do it by hand...?
its 112 pie over 9 ??
You want to find the area use Google map !
Super
Just bout 39cm²?
Edit: Fuck yeah intuituones my way to tbe rigth answer!
Please don't say: "39 centimetres squared", because that is a square with the sides 39 cm = 1521 square centimetres. Instead you should say 39 square centimetres.
Both are acceptable.
🎉🎉🎉🎉🎉❤❤❤❤ pleas more
Great
r seta
يساوي١٦
112pi/9 my guy
@@trCore that guys an npc
I got 0.39cm^2 but still can't find the mistake
from all i can see, you must’ve either scaled 70 down by multiplying by 100 into 0.7, scaled up 360 by multiplying by 100 into 36000, or scaling down 8 by dividing by 10 into 0.8
any of these values substituted into the formula compute 0.39, and it is likely you may have accidentally inputted a decimal point into the calculator somewhere, for example:
(.70/360)•(pi)•8^2
or
(70/360)•(pi)•.8^2
both compute 0.39cm^2 to two d.p.
@@joel6282ohh man.., you told all the possibilities of error to get .39
I salute you!!
I dont know that :(((((
35,1 cm sq 😅
👏
You gays can use a calculator 😮
Jesus Loves u guys
you are worng . can not find the area there is not all information.
You only need the radius and the angle to find the area of the sector, since it‘s a fraction of the area of the circle with the same radius.
'worng' 🤣🤣
I hate math :(
This is all lies
Failed maths, did we?
WTF dang how did u get the 39
Isn't 8sq 64
The formula for the area of a circle is pi × the radius². Pi is about 3.14, and the radius is 8 centimeters. That means the area of a full circle with a radious of 8 centimeters would be about 200.96 centimeters. The area we are asked to find isn't a full circle though, it is 70/360 or 7/36 of the full circle.
7/36 × 200.96 is about 39.07 centimeters which is the answer.
Using × to multiply is stupid.
If you multiply x·x using x×x, who know what you are doing?
x^2+7·x+12=0 would become
x×x+7×x+12=0, not good.
I used to write x for an unknown variable in a much fancier way than the simple x I used to indicate multiplication. I know you can't tell the difference in this comment but you could in my handwriting.
Thanks