How to find the angle of a sector using the area and radius

Discussion in 'General Discussion' started by T345, Sep 30, 2013.

1. T345

Location: Kent

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

2. [FnG]magnolia

Location: Auckland

Go to bed homework, you're drunk.

3. tomparker95

4. D.P.

Posts: 26,294

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.

5. dowie

42

6. T345

Location: Kent

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

7. Pom Pom

Posts: 42

1.21 Jiggawatts.

8. fornowagain

222d

9. Devrij

Location: Chippenham

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.

10. Elixir

Posts: 2,074

theta/360 = 70/36pi

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

11. Hyburnate

Location: NN4

Yeah, dude I pity you. Maths goes straight over my head.

12. JBod

Over 9000.

13. DN3000

14. SlyReaper

Location: Bristol, Old Blighty

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.

15. D.P.

Posts: 26,294

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.

16. Kosmiche

17. Hodders

Location: Aldbourne Wiltshire

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 .....

18. teaboy5

Location: NI

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.

Last edited: Oct 1, 2013
19. Monkeynut

Location: Cheshire

I really really had to do this. I just did.

20. JBod

Location: California

Gnnnnngggnnggghggggg..... MATHS.. MATHS