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#1 2013-08-28 04:42:03

demha
Member
Registered: 2012-11-25
Posts: 186

Circumference and Arc Length

I'm not understanding as to how to solve these. I would really appreciate a good explanation as to how to solve them. Maybe you could create a problem similar to one below and solve it step-by-step explaining what to do (I would REALLY love that smile).


What is the radius if:

1. n=30 L=1/3xy(pi)
A 6xy
B8xy
C2xy
D10xy
E 3xy
F 14xy


2. n=40 L=8/9(t)(pi)
A 20t
B5t
C9t
D18t
E 12t
F 4t


3. n=15 L=(21/36)pi
A 7
B21
C28
D62
E 56
F 14


4. n=5 L=1/2pi
A 24
B30
C45
D18
E 66
F 39


5. n=18 L=6(y)pi
A 30y
B45y
C120y
D90y
E 15y
F 60y

Last edited by demha (2013-08-28 04:42:33)


"The thing about quotes on the Internet is you cannot confirm their validity"
~Abraham Lincoln

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#2 2013-08-28 10:22:47

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,469

Re: Circumference and Arc Length

hi demha,

I'm not getting these either at the moment.  If L is an arc of a circle but what is n ?

Or can you post a diagram?

LATER EDIT:

Is n the angle at the centre?

So what fraction is that angle of a complete turn.  eg 90 degrees is one quarter of 360.

That is the same as the fraction made by arc length divided by circumference.

ie.

This seems to work in the sense that each gives one of the multi-choice answers.


Bob

View Image: demha4.gif

You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#3 2013-09-03 01:32:14

demha
Member
Registered: 2012-11-25
Posts: 186

Re: Circumference and Arc Length

This is what I got and the teacher said they were all correct. Thank you for your help big_smile

1. c correct
2. f correct
3. a correct
4. d correct
5. f correct


"The thing about quotes on the Internet is you cannot confirm their validity"
~Abraham Lincoln

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#4 2013-09-03 02:14:41

demha
Member
Registered: 2012-11-25
Posts: 186

Re: Circumference and Arc Length

I have some more from my next lesson. I would like to know if I got them right.

Area of Circles and Sectors
~What is the area of the circle if the radius is: ~


1. 4 - i said C
A 23*pi
B 18*pi
C 16*pi
D 34*pi
E 41*pi
F 60*pi


2. SQRT(3) - i said B
A 9*pi
B 3*pi
C 1*pi
D 5*pi
E 6*pi
F 7*pi


3. 7 - i said E
A 67*pi
B 53*pi
C 75*pi
D 82*pi
E 49*pi
F 34*pi


4. 6x - i said D
A 29 x^2 * pi
B 84 x^2 * pi
C 65 x^2 * pi
D 36 x^2 * pi
E 15 x^2 * pi
F 75 x^2 * pi


5. 10 - i said A
A 100*pi
B 89*pi
C 54*pi
D 72*pi
E 37*pi
F 55*pi


~What is the radius if the area of the circle is: ~


6. 9(PI) - i said F
A 7
B 2
C 5
D 6
E 4
F 3


7. 4x^2(PI) - i said B
A 5x
B 2x
C 9x
D 3x
E 6x
F 1x


8. 25(PI) - i said A
A 5
B 7
C 9
D 15
E 8
F 4


9. 81(PI) - i said A
A 9
B 3
C 5
D 7
E 2
F 6


10. 5(PI) - i said D
A sqrt 7
B sqrt 3
C sqrt 8
D sqrt 5
E sqrt 4
F sqrt 9


11. (9/16)PI - i said E
A 7/6
B 3/1
C 5/2
D 9/5
E 3/4
F 4/1


12. 25y^2(PI) - i said D
A 9y
B 3y
C 6y
D 5y
E 2y
F 10y


13. 16z^2(PI) - i said C
A 9z
B6z
C4z
D7z
E 5z
F 2z


14. t^2(PI) - i said D
A 3.146
B 5
C 2
D t
E 9
F 7


15. (PI) - i said E
A 2
B 6
C 8
D 3
E 1
F 5


~What is the area of the sector if the radius is 6 and the degree measure is: ~


16. 26 - i said C
A 1.9*pi = 9.523
B 6.7*pi = 3.491
C 2.6*pi = 8.168
D 5.1*pi = 7.054
E 9.2*pi = 3.115
F 7.8*pi = 1.274


17. 30 - i said F
A 6*pi
B 5*pi
C 9*pi
D 1*pi
E 6*pi
F 3*pi


18. 50 - i said A
A 5*pi
B 4*pi
C 3*pi
D 9*pi
E 2*pi
F 7*pi


19. 90 - i said D
A 8*pi
B 3*pi
C 1*pi
D 9*pi
E 7*pi
F 2*pi


20. 120 - i said F
A 23*pi
B 74*pi
C 89*pi
D 24*pi
E 59*pi
F 12*pi


"The thing about quotes on the Internet is you cannot confirm their validity"
~Abraham Lincoln

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#5 2013-09-03 03:44:47

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,469

Re: Circumference and Arc Length

hi demha

I'm really pleased you got the others right.  Excellent!  OK, let's have a look at the new ones:


Area of Circles and Sectors
~What is the area of the circle if the radius is: ~


1. 4 - i said C
A 23*pi
B 18*pi
C 16*pi
D 34*pi
E 41*pi
F 60*pi

Correct. 

2. SQRT(3) - i said B
A 9*pi
B 3*pi
C 1*pi
D 5*pi
E 6*pi
F 7*pi

Correct! 

3. 7 - i said E
A 67*pi
B 53*pi
C 75*pi
D 82*pi
E 49*pi
F 34*pi

Correct! 

4. 6x - i said D
A 29 x^2 * pi
B 84 x^2 * pi
C 65 x^2 * pi
D 36 x^2 * pi
E 15 x^2 * pi
F 75 x^2 * pi

Correct! 

5. 10 - i said A
A 100*pi
B 89*pi
C 54*pi
D 72*pi
E 37*pi
F 55*pi

Correct!   

~What is the radius if the area of the circle is: ~


6. 9(PI) - i said F
A 7
B 2
C 5
D 6
E 4
F 3

Correct!   

7. 4x^2(PI) - i said B
A 5x
B 2x
C 9x
D 3x
E 6x
F 1x

Correct!   


8. 25(PI) - i said A
A 5
B 7
C 9
D 15
E 8
F 4

Correct!   


9. 81(PI) - i said A
A 9
B 3
C 5
D 7
E 2
F 6

Correct!   

10. 5(PI) - i said D
A sqrt 7
B sqrt 3
C sqrt 8
D sqrt 5
E sqrt 4
F sqrt 9

Correct!   

11. (9/16)PI - i said E
A 7/6
B 3/1
C 5/2
D 9/5
E 3/4
F 4/1

Correct!   

12. 25y^2(PI) - i said D
A 9y
B 3y
C 6y
D 5y
E 2y
F 10y

Correct!   

13. 16z^2(PI) - i said C
A 9z
B6z
C4z
D7z
E 5z
F 2z

Correct!   

14. t^2(PI) - i said D
A 3.146
B 5
C 2
D t
E 9
F 7

Correct!   

15. (PI) - i said E
A 2
B 6
C 8
D 3
E 1
F 5

Correct!   

~What is the area of the sector if the radius is 6 and the degree measure is: ~


16. 26 - i said C
A 1.9*pi = 9.523
B 6.7*pi = 3.491
C 2.6*pi = 8.168
D 5.1*pi = 7.054
E 9.2*pi = 3.115
F 7.8*pi = 1.274

Correct!   


17. 30 - i said F
A 6*pi
B 5*pi
C 9*pi
D 1*pi
E 6*pi
F 3*pi

Correct!   

18. 50 - i said A
A 5*pi
B 4*pi
C 3*pi
D 9*pi
E 2*pi
F 7*pi

Correct!   

19. 90 - i said D
A 8*pi
B 3*pi
C 1*pi
D 9*pi
E 7*pi
F 2*pi

Correct!   

20. 120 - i said F
A 23*pi
B 74*pi
C 89*pi
D 24*pi
E 59*pi
F 12*pi

Correct!   

That's excellent.  You have certainly done well with these.  smile   

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#6 2013-09-03 04:24:36

demha
Member
Registered: 2012-11-25
Posts: 186

Re: Circumference and Arc Length

Ah, thank you once again Mr. Bob for spending your time to check these for me wink

Sent in the lesson and got 10.000.


"The thing about quotes on the Internet is you cannot confirm their validity"
~Abraham Lincoln

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