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# Surface area and sector area GCSE Watch

1. (Original post by Tinkletea)
I thought the formula to find the area of a sector was theta / 360 x pi x r^2?
oh sorry, I used radians.
2. (Original post by Tinkletea)
I thought the formula to find the area of a sector was theta / 360 x pi x r^2?
Yes, if you're working in degrees
3. I seem to use a different method which I find easier, I will input and I do apologise if I am incorrect, I am self teaching Maths and so I do get muddled at times. But this what I got.

To work out feta =

Arc length = feta /360 x 2 x pi x r. We know Arc length = 15. Therefore

15 = feta / 360 x 2 x pi x r.

To work this out, multiply arc length by 360 and divide by 2 x pi x r =

15 x 360 / 2 x pi x 10 = 85.9436692696 = feta.

Therefore you can now work the area out.

Area of sector = feta / 360 x pi x r^2 therefore =

85.9436692696 / 360 x pi x 10^2 = 75^2.

I find this method very easy.
4. (Original post by Tinkletea)
I seem to use a different method which I find easier, I will input and I do apologise if I am incorrect, I am self teaching Maths and so I do get muddled at times. But this what I got.

To work out feta =

Arc length = feta /360 x 2 x pi x r. We know Arc length = 15. Therefore

15 = feta / 360 x 2 x pi x r.

To work this out, multiply arc length by 360 and divide by 2 x pi x r =

15 x 360 / 2 x pi x 10 = 85.9436692696 = feta.

Therefore you can now work the area out.

Area of sector = feta / 360 x pi x r^2 therefore =

85.9436692696 / 360 x pi x 10^2 = 75^2.

I find this method very easy.
For the love of god

It is THETA
5. (Original post by Tinkletea)
I seem to use a different method which I find easier, I will input and I do apologise if I am incorrect, I am self teaching Maths and so I do get muddled at times. But this what I got.

To work out feta =

Arc length = feta /360 x 2 x pi x r. We know Arc length = 15. Therefore

15 = feta / 360 x 2 x pi x r.

To work this out, multiply arc length by 360 and divide by 2 x pi x r =

15 x 360 / 2 x pi x 10 = 85.9436692696 = feta.

Therefore you can now work the area out.

Area of sector = feta / 360 x pi x r^2 therefore =

85.9436692696 / 360 x pi x 10^2 = 75^2.

I find this method very easy.
More likely to lose accuracy there if you're not careful, but as long as you take care.
6. Yeah I agree. Joys of 'Ans' on my calculator though.
7. (Original post by Tinkletea)
I seem to use a different method which I find easier, I will input and I do apologise if I am incorrect, I am self teaching Maths and so I do get muddled at times. But this what I got.

To work out feta =

Arc length = feta /360 x 2 x pi x r. We know Arc length = 15. Therefore

15 = feta / 360 x 2 x pi x r.

To work this out, multiply arc length by 360 and divide by 2 x pi x r =

15 x 360 / 2 x pi x 10 = 85.9436692696 = feta.

Therefore you can now work the area out.

Area of sector = feta / 360 x pi x r^2 therefore =

85.9436692696 / 360 x pi x 10^2 = 75^2.

I find this method very easy.
Thanks for that, it explained to me that you find out Theta, I though it was a symbol for a number like pi.

Just need to remember the equation you used now.

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8. (Original post by yellowcopter)
Thanks for that, it explained to me that you find out Theta, I though it was a symbol for a number like pi.

Just need to remember the equation you used now.

Posted from TSR Mobile
It's basically asking what fraction of the circle it has for theta.

x/360 = the fraction of the circle it is.

Pi * r^2 = area of a full circle
9. (Original post by L'Evil Fish)
It's basically asking what fraction of the circle it has for theta.

x/360 = the fraction of the circle it is.

Pi * r^2 = area of a full circle
What fraction of the circle does that angle start at? 'Fraction of the circle it has theta' doesn't make sense to me.

What's x in x/360? So confused! My teacher never teaches us above D/C grade, very annoying and confuses me when I try to do higher grade questions!

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10. (Original post by yellowcopter)
What fraction of the circle does that angle start at? 'Fraction of the circle it has theta' doesn't make sense to me.

What's x in x/360? So confused! My teacher never teaches us above D/C grade, very annoying and confuses me when I try to do higher grade questions!

Posted from TSR Mobile
For notational purposes I believe L'Evil Fish has used x instead of theta. the principle is however the same.
11. (Original post by yellowcopter)
What fraction of the circle does that angle start at? 'Fraction of the circle it has theta' doesn't make sense to me.

What's x in x/360? So confused! My teacher never teaches us above D/C grade, very annoying and confuses me when I try to do higher grade questions!

Posted from TSR Mobile
Well the sector.

x is the angle should have made ir clearer, sorry
12. (Original post by L'Evil Fish)
Well the sector.

x is the angle should have made ir clearer, sorry
MAKES SOOOOOO MUCH MORE SENSE than using theta, THANK YOU!

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13. (Original post by yellowcopter)
MAKES SOOOOOO MUCH MORE SENSE than using theta, THANK YOU!

Posted from TSR Mobile
Whatever floats your boat (or helicopter...)
14. (Original post by yellowcopter)
Thanks for that, it explained to me that you find out Theta, I though it was a symbol for a number like pi.

Just need to remember the equation you used now.

Posted from TSR Mobile
Thats ok

The way I remember it is by remembering by knowing the basics behind it:

Arc length is the distance around the sector, what is circumference? the distance around the circle. Therefore to find out the circumference (arc length) of the sector, you just do theta / 360 (the angle of the sector, if given, divided by a full circle (360) x 2 x pi x r. What is 2 x pi x r? why its the formula of working out a circumference. I found it took me a little while to get that, but once I did its stuck. Just remember arc length is just the same as the circumference( although do remember the sides if asked for the perimeter of the sector), therefore its much easier to remember the formula associated with the arc length

Same goes for the area, use the angle (if given) divided by the full circle, x pi x r^2... pi x r^2? the area of a circle.

I'm not being patronising by the way, I have found it very difficult, it took me a while to get this. I left school early and therefore didn't get taught much, especially to this standard so I know its so important to really get whats obvious to others, first before you can work on the harder stuff.

Once you understand the concepts behind it, it will be easier to try harder questions.

If you are given the angle and radius, but not the arc length, look at the formula for finding arc length.

Arc length = theta / 360 x (2 x pi x r). Since you know the angle, you can plug that in, work it out and you will find the arc length.

To find the angle, if you are given arc length.

As above, if you know the arc length you can find the angle just by rearranging what you know.
theta / 360 x 2 x pi x r = arc length. So to get feta on its own you need multiply the arc length by 360 and divide by 2 x pi x r. then of course when you know the angle, you can plug it into the area formula to find the area.

Same goes if you know the area and radius. Look at the formula and see what you can do to find theta. = Area = theta / 360 x pi x r^2. This is very similar to above, all you would need to do is multiply the area by 360 and divide it by pi and r^2.

If you have the area and angle, you can find the radius by doing some rearranging again.

Again, please don't see this as patronising as it took me a while of sitting watching videos etc to get it because I did not know the basics and therefore I was running before I could jump. I would definitely recommend youtube, there is some very good videos on there. When I first looked at these, I thought it was going to be another 'ill leave that one out' like vectors, but watched a few videos and I get it now.

HTH

Edit: Here is the video that really 'drilled it' for me. http://www.youtube.com/watch?v=WIpdloZ0v78

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