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## #1 2006-06-29 02:21:48

RickyOswaldIOW
Member
Registered: 2005-11-18
Posts: 212

### Sector Perimeter

I have a question here asking for the Perimeter of a shaded section of a circle:

The full circle is shown with center O.  One sector is labled with a radius of 20 and angle Pi/2 (90 degrees).  The rest of the circle is shaded and that is the part I need to work out the perimeter of.
I know that a full circle is 2Pi radians (360 degrees) and since the unshaded sector is Pi/2 radians I can deduce
2Pi - Pi/2 = 3Pi/2 (270 degrees)

Now I just use the regular formula for working out the arc length which is
s = rθ
(let θ = the angle in radians)
s = 20 * 3Pi/2 = 60Pi/2 = 94.2 (3.s.f)

Is this correct? The answers at the back of the book states134.2!

Aloha Nui means Goodbye.

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## #2 2006-06-29 02:24:24

RickyOswaldIOW
Member
Registered: 2005-11-18
Posts: 212

### Re: Sector Perimeter

Do I need to set my calculator to radian mode?  How do I do this? It's a casio fx-83wa.

Aloha Nui means Goodbye.

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## #3 2006-06-29 02:37:01

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

### Re: Sector Perimeter

Notice something.  Your answer is off by 134.2 - 94.2 = 40.  Coincidence?  I think not.  That number should sound familiar.  What piece are you missing?

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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## #4 2006-06-29 02:40:55

RickyOswaldIOW
Member
Registered: 2005-11-18
Posts: 212

### Re: Sector Perimeter

40? Hum... I can see that the first sector (with the angle Pi/2) has an arc length of 10Pi and the other sector has an arc of 30Pi, that adds up to 40Pi  but I do not see how it is related?

P.S. This is the second question I've ever done of this module so I do not know much about it

Last edited by rickyoswaldiow (2006-06-29 02:42:34)

Aloha Nui means Goodbye.

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## #5 2006-06-29 02:45:19

RickyOswaldIOW
Member
Registered: 2005-11-18
Posts: 212

### Re: Sector Perimeter

I could look at it this way:
The first sector has angle Pi/2 and radius 20. s=rθ=20*Pi/2=10Pi

Since Pi/2 = 90 degrees which is 1/4 of the full circle, the shaded sector is the other 3/4 of the circle.  1/4 of the circle = 10Pi and thus 3/4 of it would = 30Pi, 94.2.

Aloha Nui means Goodbye.

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## #6 2006-06-29 02:47:51

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

### Re: Sector Perimeter

40 = 2*20 = 2*r.  You have to not only measure the arc length but also the...

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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## #7 2006-06-29 02:50:16

RickyOswaldIOW
Member
Registered: 2005-11-18
Posts: 212

### Re: Sector Perimeter

Aha! Of course
The perimeter stretches along the two straight edges of the unshaded sector and not just round the arc of the shaded area.

Aloha Nui means Goodbye.

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## #8 2006-06-29 05:32:08

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

### Re: Sector Perimeter

Right!

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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