Calculate the perimeter of the outside of the lane

bumblebee123

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question: the diagram shows the markings of a running track lane. the inside of the lane consists of two straight lines, each of length d metres and two semicircles, each with a radius of r metres. the perimeter of the inside of the lane is 400 metres.

a) explain why 2 π r + 2d = 400

I think I understand this. The circumference of the inner semicircles is going to make a circle, so 2 π r. The lines = d and there are two lines so their perimeter is 2d.

b) the lane is 1 metre wide. the outside lane consists of two straight lines, each of length d metres, and two semicircles. Calculate the perimeter of the outside of the lane

how would I figure this out? any help would be really appreciated :)
 
You should be able to find part of the perimeter. The two lines have a length of ?
For each semicircle of the outer track what is the radius? Remember that the outer track is always (including the semicircular region!) 1 meter away from the inner track. Note that the centers for the inner and outer tracks are the same.
 
You should be able to find part of the perimeter. The two lines have a length of ?
For each semicircle of the outer track what is the radius? Remember that the outer track is always (including the semicircular region!) 1 meter away from the inner track. Note that the centers for the inner and outer tracks are the same.

2π ( 1 + r ) + 2d

2π + 2π r + 2d
 
Looks good to me, but is still incomplete. What is the exact perimeter of the outer portion of the track?

2π r + 2d = inside perimeter = 400

2π + 2π r + 2d = outside perimeter

6.283185307 + 2π r + 2d = ouside perimeter

6.283185307 +400 = outside perimeter

outside perimeter = 406 m ( 3s.f.)

yes! this is the answer! thanks! :)
 
2π r + 2d = inside perimeter = 400

2π + 2π r + 2d = outside perimeter

6.283185307 + 2π r + 2d = ouside perimeter

6.283185307 +400 = outside perimeter

outside perimeter = 406 m ( 3s.f.)

yes! this is the answer! thanks! :)
No, sorry but that is not the exact answer. It may be a good approximation but still it is an approximation. I did ask for the exact answer-I chose my words carefully. The exact answer is 2π + 400 ~ 406.283185307
 
No, sorry but that is not the exact answer. It may be a good approximation but still it is an approximation. I did ask for the exact answer-I chose my words carefully. The exact answer is 2π + 400 ~ 406.283185307

In the question, at the bottom, it said (to 3 significant figures ). sorry, I don't think I included that in the original post!:)
 
part c) says when the width of the lane is w metres, the perimeter of the outside of the lane is p metres. find, in terms of w, a formula for p. give your answer as simply as possible

I've been looking at this all morning, and I just can't get my head around it! which part os the width, is it cutting the whole track in half vertically?
 
In the original problem, they tell you that the width is 1 meter. That is what "width" means here, too -- the measurement marked as 1 in the picture, which is the width of the lane itself, not of the whole track.

So do the same work as before, but replacing that 1 with w.

It's really important to give the entire problem from the start; it's emphasized in the submission guidelines. Now you see why. If there's anything else you omitted, be sure to tell us the whole thing.
 
In the original problem, they tell you that the width is 1 meter. That is what "width" means here, too -- the measurement marked as 1 in the picture, which is the width of the lane itself, not of the whole track.

So do the same work as before, but replacing that 1 with w.

It's really important to give the entire problem from the start; it's emphasized in the submission guidelines. Now you see why. If there's anything else you omitted, be sure to tell us the whole thing.

okay, I will do next time- I just assumed I'd be able to figure out the other part of the question myself.

= 2π ( w + r ) + 2d
= 2πw + 2πr + 2d
= 2πw + 400 ( this is correct! )

thanks!
 
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