# Calculating perimeter

1. Jun 21, 2011

### Femme_physics

1. The problem statement, all variables and given/known data

http://img94.imageshack.us/img94/9216/thethingy.jpg [Broken]

Through a circle roundabout whose radius is 220 meters, they constructed a sidewalk in width of 30 meters. Calculate the perimeter of the sidewalk.

3. The attempt at a solution

perimeter of a circle equation: 2 x pi x R

So 220+30 = 250

2 x pi x 250 = 1570.8 squared meters.

And yet I'm told the answer is 880 meters.

Last edited by a moderator: May 5, 2017
2. Jun 21, 2011

### tiny-tim

Hi Femme_physics!

I think the sidewalk must be straight across the middle.

(and don't forget it has two sides )

3. Jun 21, 2011

### I like Serena

Hi Fp!

Is it possible that the roundabout has a diameter of 220 m, instead of a radius of 220 m?

4. Jun 21, 2011

### Femme_physics

Hi tiny-timmy! :)

How confusing -- since they drew another circle that says "sidewalk" so I thought the sidewalk is round.

So it really should be

(250+30) x 2 = 560

Hmm...still off the mark

5. Jun 21, 2011

### Femme_physics

Hi ILS! :)

You're right! I was lost in translation!

If I presume the sidewalk is round it should be

2 x pi x (250/2) = 785.398

Argh no still off

6. Jun 21, 2011

### I like Serena

Do you have half a sidewalk around the roundabout?

Isn't that a bit narrow to walk on?

A couple of mistakes wouldn't be able to walk next to each other!

Last edited: Jun 21, 2011
7. Jun 21, 2011

### Femme_physics

30 meters width is a bit narrow?

And why half? That formula relates the entire perimeter based on radius

8. Jun 21, 2011

### I like Serena

So what is the proper radius?

First of the roundabout and then with the sidewalk included?

9. Jun 21, 2011

### AJKing

Hey Femme, the question is a little vague in this regard: is the sidewalk straight or circular?

If the side walk is straight:
$2*(220*x)+2*(30*y) = 880$
I don't have all the math figured out (hence the variables), but just work with me here.

The perimeter of a rectangular object is:
$2*l+2*w$
No big deal. We know that.

We also know that an object with a length of 440m (our diameter), and no width (but 2 sides, somehow), has a perimeter of 880m.

But, when you place a rectangle of any width over top of a circle's center, you have 4 "ears" hanging off of the edge which are dead weight in this simulation.
If the sidewalk is straight, I'm willing to wager that the changed length of the 440m diameter being offset left and right by 15 meters each is balanced by the arc-length of the two ends of the sidewalk in order to still equal 880m, since only the width is 30m, not the arc-lengths.

However, if the sidewalk is circular and 30 meters wide and equals 880m in perimeter, then we can just write an equation to solve for its radii.

$880 = 2r_{1}\pi + 2(r_{1}+30)\pi$

Unless I was careless, this works out to:

$r_{1} \approx 55m$

So, we've got to be getting some misinformation here.

Last edited: Jun 21, 2011
10. Jun 21, 2011

### tiny-tim

Hi ILS!
Yup, it's the diameter

(220 + 60) * 22/7

11. Jun 21, 2011

### AJKing

Don't you need 2 circumferences to determine the perimeter of a "donut" shape?

12. Jun 21, 2011

### tiny-tim

Hi AJKing!
Yup!

Rubbish question, isn't it?

13. Jun 21, 2011

### AJKing

Lol, quite so!

14. Jun 21, 2011

### Femme_physics

The fact that the perimeter equals 880 is not something I know -- it's just from the solution manual, that's what I need to find

15. Jun 21, 2011

### ehild

You get that perimeter if you calculate with 220 m as the diameter of the inner circle. So what is the diameter of the outer circle?

ehild

16. Jun 21, 2011

### Staff: Mentor

If you were going to provide walkers with a short-cut over a circular patch of precious grass, you would provide 2 intersecting straight paths, one running N-S and the other E-W. (you get the picture, since it's an intersection of some description)

If you then wanted to border that walking area with a distinctive coloured paving stone, you would need to know that perimeter, i.e., the sum of the lengths of all 12 sides. I make this 8.8 x 102 metres.

17. Jun 23, 2011

### I like Serena

Hey fp!

Did you already solve this problem?
Were you able to work through the posts of the different people and work out what the solution is?

18. Jun 23, 2011

### Femme_physics

Hi ILS :)

I didn't, but we already had the math test 2 days ago and now I got some other priorities.

So thanks everyone for your replies and the great help you were giving!! I just skipped a similar question that was on the test and took a similar one to the "diamond" shape that I also posted here at about the same time. That was easier :)

Thanks for caring!

19. Jun 24, 2011

### Ouabache

I believe tiny-tim & ILS have already made a reasonable guess at the author's intent.
Summarizing: Around a circular roundabout whose diameter is 220 meters,
is constructed a circular sidewalk of width 30 meters.
Calculate the outer perimeter of the sidewalk.

The diameter of the inner-circle is 220m
the width of the sidewalk is given = 30m.
The perimeter $= 2 \pi r = 2 \pi (\frac {220}{2}+30)$.
(or if you prefer perimeter $= \pi d$) as tiny-tim indicated above).