Convert area o circle to rectangle

[qim]

It's probably too early in the morning and the brain hasn't woken up yet....

I am planning to insert a tube of diameter 12cm into a chimney with only 10cm depth, I will have to squash it to make it fit into what will become a rectangular form. You squeeze it in and obviously( ?'?? ) the width will be larger than the original 12cm but...

pi . r2 = 113 cm2

and if the shorter side of the rectangle is 10cm and the total area is 113 cm2, then the wider side becomes 11,3 cm... (less than the original???)

I expect that the maths are right and that the answer to the puzzle is that the tube will never be completely a rectangle as the corners are still part of a round figure,,,

Can you tell me I am not going mad?

Tahanks

qim

 

[stapel]

I am planning to insert a tube of diameter 12cm into a chimney with only 10cm depth, I will have to squash it to make it fit into what will become a rectangular form. You squeeze it in and obviously( ?'?? ) the width will be larger than the original 12cm but...

pi . r2 = 113 cm2

and if the shorter side of the rectangle is 10cm and the total area is 113 cm2, then the wider side becomes 11,3 cm... (less than the original???)

I'm not sure what you're saying here...?

If you have a liner (the "tube"?) which has a perimeter (being, in this case, the circumference) of about 38 centimeters, and you're trying to insert it into a brick column (being the inside of the chimney) that has a perimeter of 40 centimeters, then you'll likely need to square out the "tube" first, in order to slide the liner down inside.

Eliz.

 

[Dr.Peterson]

It's probably too early in the morning and the brain hasn't woken up yet....

I am planning to insert a tube of diameter 12cm into a chimney with only 10cm depth, I will have to squash it to make it fit into what will become a rectangular form. You squeeze it in and obviously( ?'?? ) the width will be larger than the original 12cm but...

pi . r2 = 113 cm2

and if the shorter side of the rectangle is 10cm and the total area is 113 cm2, then the wider side becomes 11,3 cm... (less than the original???)

I expect that the maths are right and that the answer to the puzzle is that the tube will never be completely a rectangle as the corners are still part of a round figure,,,

Can you tell me I am not going mad?

Tahanks

qim

As I understand it, the tube in its original state has an area of 113 cm^2, but when you change its shape, it will be its perimeter, not its area, that remains the same (more or less).

If the rectangular chimney has the same cross-sectional area as the tube, then its width is 11.3 cm; but do you have any reason to think that is true? What are the actual dimensions of the chimney?

On the other hand, the chimney's perimeter would then be 42.3 cm, compared to the tube's 12 pi = 37.7 cm, so in principle it could be possible to distort the tube to fit.

Now, if you squeeze the tube into an elliptical form, then reducing one dimension from 12 to 10 cm would increase the other to something more than 12 cm (the calculation isn't easy). But I can't tell if that would fit the chimney, or whether the reduction in area would be a problem.

 

[qim]

Thank you both. My post was about a mathematical misunderstanding on my part (not a need for help to do the actual repair job, which in fact had already been done by the time I posted). But, yes, your replies helped me wake up and understand that my maths were totally wrong as by distorting a tube what really mattered was the perimeter and not the area...

Thank you