Overclockers UK Forums > Life > General Discussion How to find the angle of a sector using the area and radius

 30th Sep 2013, 20:09 #1 T345 Soldato     Joined: Oct 2011 Location: Kent Posts: 5,738 How to find the angle of a sector using the area and radius Hi guys, another maths question. I am having trouble finding the method to do this, online and in my head. The question is: A sector with radius 6cm has an area 70cm sq. Calculate the angle of the sector Theta. I am struggling, and if anyone can show me how to do it, I will be grateful. Thanks Bakht i5 3570k | MSI Z68A-GD65 | 4gb RAM | Radeon HD 6950 | FD Arc R2
 30th Sep 2013, 20:15 #2 [FnG]magnolia Capodecina   Joined: Aug 2007 Location: Auckland Posts: 23,632 Go to bed homework, you're drunk.
30th Sep 2013, 20:17   #3
tomparker95
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Quote:
 Originally Posted by [FnG]magnolia Go to bed homework, you're drunk.

30th Sep 2013, 20:18   #4
D.P.
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Quote:
 Originally Posted by T345 Hi guys, another maths question. I am having trouble finding the method to do this, online and in my head. The question is: A sector with radius 6cm has an area 70cm sq. Calculate the angle of the sector Theta. I am struggling, and if anyone can show me how to do it, I will be grateful. Thanks Bakht

The answer is very easy, I will let you work it out form basic principles:
A) What is the formula to find the area of a circle?
b) what is the radius of the circle given in the questions?
C) What is the fractional area of the sector given in the question?
D) If you cut a circle n half what would the area of the 2 half be and what are the angles of the 2 sectors?
E) Out of 360 degrees the sector must have angle with a fraction proportional to the areas.

 30th Sep 2013, 20:34 #5 dowie Capodecina     Joined: Jan 2008 Posts: 22,460 42
30th Sep 2013, 20:35   #6
T345
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Quote:
 Originally Posted by D.P. The answer is very easy, I will let you work it out form basic principles: A) What is the formula to find the area of a circle? b) what is the radius of the circle given in the questions? C) What is the fractional area of the sector given in the question? D) If you cut a circle in half what would the area of the half be and what are the angles of the 2 sectors? E) Out of 360 degrees the sector must have angle with a fraction proportional to the areas.
Ok, so I got the area of the entire circle (36pi).
The fractional area would be
70/36pi.
I don't know what you mean in D though

i5 3570k | MSI Z68A-GD65 | 4gb RAM | Radeon HD 6950 | FD Arc R2

 30th Sep 2013, 20:36 #7 Pom Pom PermaBanned   Joined: Aug 2013 Posts: 42 1.21 Jiggawatts.
 30th Sep 2013, 20:42 #8 fornowagain Sgarrista     Joined: Nov 2004 Location: UK Posts: 9,663 222d
30th Sep 2013, 20:43   #9
Devrij
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Quote:
 Originally Posted by T345 Ok, so I got the area of the entire circle (36pi). The fractional area would be 70/36pi. I don't know what you mean in D though
He's saying half a circle would be 18pi, and the angle of that sector is 180 degrees. So work out what the angle is using the fraction that 77/36pi represents.

30th Sep 2013, 20:49   #10
Elixir
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Quote:
 Originally Posted by T345 Ok, so I got the area of the entire circle (36pi). The fractional area would be 70/36pi. I don't know what you mean in D though
theta/360 = 70/36pi

The angle will be the same fraction of the entire circle as the area is.

 30th Sep 2013, 20:51 #11 Hyburnate Capodecina     Joined: Jul 2011 Location: NN4 Posts: 12,846 Yeah, dude I pity you. Maths goes straight over my head.
 30th Sep 2013, 20:53 #12 JBod Soldato   Joined: Sep 2007 Location: California Posts: 5,008 Over 9000.
30th Sep 2013, 20:56   #13
DN3000
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Quote:
 Originally Posted by dowie 42

 30th Sep 2013, 21:05 #14 SlyReaper Soldato     Joined: Apr 2008 Location: Hotwells, Bristol Posts: 5,852 The area of a full circle of radius 6 is 36*pi. Yours isn't a full circle, it has area 70. So the fraction of the circle you have is 70/(36*pi). Multiply that by 360, and you have your answer in degrees. If you want to show off to your maths teacher, give the answer in radians instead. Please read the FAQ regarding signature sizes
30th Sep 2013, 21:28   #15
D.P.
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Quote:
 Originally Posted by T345 Ok, so I got the area of the entire circle (36pi). The fractional area would be 70/36pi. I don't know what you mean in D though
Im just trying to get you to think. If you cut a circle in half then each half would have an angle of 180 degrees which is half of 360 and the area of each half is obviously half the original entire circle.

If you understand why that works then it is obvious how the angle of the sector and area relate to the original circle.

 30th Sep 2013, 21:28 #16 Kosmiche Suspended     Joined: Oct 2009 Location: North Wales Posts: 14,041
 30th Sep 2013, 21:59 #17 Hodders Mobster     Joined: Oct 2002 Location: Aldbourne Wiltshire Posts: 3,336 A circle of radius 6cm has an area of pi * 6 * 6 (pi r^2) The area of the cake slice is 70cm The proportion of the whole cake (360 degrees) is 360 * 70 / (pi * 36) Now please tell me that this is year 7 stuff .....
30th Sep 2013, 23:27   #18
teaboy5
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Quote:
 Originally Posted by Hodders A circle of radius 6cm has an area of pi * 6 * 6 (pi r^2) The area of the cake slice is 70cm The proportion of the whole cake (360 degrees) is 360 * 70 / (pi * 36) Now please tell me that this is year 7 stuff .....
Year 7 really ?

Why do people always put people down who don't understand math? Not every is great it and believe it or not, some people have little to no time for math, bar say passing it at GCSE level.

Quote:
 Originally Posted by [TW]Fox I always indicate but only becuase the high quality, solid feel of my indicator switches turns me on.
Last edited by teaboy5; 30th Sep 2013 at 23:32.

30th Sep 2013, 23:37   #19
Monkeynut
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Quote:
 Originally Posted by teaboy5 Year 7 really ? Why do people always put people down who don't understand maths? Not every is great it and believe it or not, some people have little to no time for mathS, bar say passing it at GCSE level.
I really really had to do this. I just did.

30th Sep 2013, 23:54   #20
JBod
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Quote:
 Originally Posted by teaboy5 Year 7 really ? Why do people always put people down who don't understand math? Not every is great it and believe it or not, some people have little to no time for math, bar say passing it at GCSE level.
Gnnnnngggnnggghggggg..... MATHS.. MATHS

 1st Oct 2013, 00:07 #21 d_brennen Capodecina     Joined: Jan 2009 Location: Aquilonem Londinensi Posts: 12,920 Did someone say meth?
1st Oct 2013, 04:46   #22
DN3000
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Quote:
 Originally Posted by d_brennen Did someone say meth?
Spoiler:

 1st Oct 2013, 06:01 #23 Rich_L Capodecina     Joined: Oct 2002 Location: Santa Barbara, Californee Posts: 18,162 Ok so you cut a cake in two and you still have one cake but two halves. So if you cut a sandwich in half do you have two sandwiches or two half sandwiches? Please state your working preferably in MS Paint.
 1st Oct 2013, 06:50 #24 [FnG]magnolia Capodecina   Joined: Aug 2007 Location: Auckland Posts: 23,632 There's this plane on a treadmill, right, and
 1st Oct 2013, 08:29 #25 jonnyp1993 Wise Guy     Joined: Feb 2013 Location: Leeds Posts: 1,618 My brain hurts just reading this Please read the rules and FAQ regarding signature sizes why ?, If i get it right.. its wrong! So you get a sig that wont be removed - who did this ?, Show yourself! - It wasn't me!
6th Nov 2013, 22:14   #26
Acme
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I don't miss school y'know.

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 Originally Posted by Phate I have the motivated of a sedated sloth today.

 6th Nov 2013, 22:19 #27 Theophany PermaBanned     Joined: Sep 2010 Location: PermaProbation. Posts: 10,052
 6th Nov 2013, 22:25 #28 cm1179 Wise Guy   Joined: Sep 2009 Posts: 2,495 what if the cake was a square shaped cake?
6th Nov 2013, 22:31   #29
StriderX
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Quote:
 Originally Posted by cm1179 what if the cake was a square shaped cake?
What if the cake didn't actually exist and this question was in fact invalid?

6th Nov 2013, 22:35   #30
bitslice
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Quote:
 Originally Posted by StriderX What if the cake didn't actually exist and this question was in fact invalid?
Whaa?
a minute ago we were talking pie and I was interested and paying attention, now we are talking existential cake?
This is all too fast for me, I'm not that kind of boy