Determine diameter of a circle from a straight line

[rightbraincreative]

I'm sure this is a basic high school problem, but I don't know the answer, hence I am here. I need to bend a straight pipe into a circle and need to know how to figure out how long the pipe needs to be to create a 4 foot diameter circle. Any help would be greatly appreciated.

 

[pka]

I'm sure this is a basic high school problem, but I don't know the answer, hence I am here. I need to bend a straight pipe into a circle and need to know how to figure out how long the pipe needs to be to create a 4 foot diameter circle. Any help would be greatly appreciated.

The circumference of a circle is \(\displaystyle \pi\cdot D\). A good approximation is "three times around as it is across"
\(\displaystyle \pi\approx 3.1415\).

 

[lookagain]

The circumference of a circle is \(\displaystyle \pi\cdot D\). A good approximation is "three times around as it is across"
\(\displaystyle \pi\approx 3.1415\).

As \(\displaystyle \pi \ \) = 3.141592..., the rounded value of \(\displaystyle \ \pi \ \ = \ \ 3.1416 \ \ \) to four decimal places.

 

[rightbraincreative]

The circumference of a circle is \(\displaystyle \pi\cdot D\). A good approximation is "three times around as it is across"
\(\displaystyle \pi\approx 3.1415\).

So, without getting into too many decimal points, my 4 foot diameter circle can be created by multiplying pi times the diameter I need. 3.14 x 4= 12.56. My pipe needs to be roughly 12 and a half feet to make a four foot hoop. Thank you all for your expertise. This will help me finish an art project I am working on. I knew pi was involved in the equation, but not how. I guess I should have paid more attention in math classes and less attention to art. But, in the end, art is what pays my bills each month.

 

[stapel]

It should be noted, of course, that these are "ideal" mathematical computations on "ideal" geometrical objects. When dealing with real-world physical objects, allowances usually need to be made for width, depth, cutting losses, etc. For instance, if the stated desired diameter refers to the inner diameter of the physical object, then allowances must be made for stretching of the material, along with the depth of the material (diameter of the pipe, perhaps?), with the computations adjusted to account for the fact that a pipe cut to form the desired circle on the inner edge may have a gap on the outer edge. And crushing or crumpling may reduce the expected inner measure, after bending, as well.

 

[rightbraincreative]

It should be noted, of course, that these are "ideal" mathematical computations on "ideal" geometrical objects. When dealing with real-world physical objects, allowances usually need to be made for width, depth, cutting losses, etc. For instance, if the stated desired diameter refers to the inner diameter of the physical object, then allowances must be made for stretching of the material, along with the depth of the material (diameter of the pipe, perhaps?), with the computations adjusted to account for the fact that a pipe cut to form the desired circle on the inner edge may have a gap on the outer edge. And crushing or crumpling may reduce the expected inner measure, after bending, as well.

Thank you for the additional thoughts. Yes, these are conditions I need to factor in to my design.