SOLUTION: What is the exact diameter in centimetres of the largest semi-circle that could be made from 1m of wire?

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Question 1179987: What is the exact diameter in centimetres of the largest semi-circle that could be made from 1m of wire?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.

It is  2%2Fpi  meters,


where  pi = 3.14...  is the ratio of a circle length to its diameter.

Solved, answered and explained.



Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The circumference of a circle is pi times the diameter; half the circumference is (pi/2) times the diameter.

If that half circumference is 1m, then

%28pi%2F2%29%28d%29=1
d=1%2F%28pi%2F2%29=2%2Fpi

And the answer is as shown by the other tutor.

That answer uses the interpretation that the "semi-circle" being formed is an open figure, consisting of only the curved part of the semicircle.

Another possible interpretation is that the figure being formed is a closed semi-circle, including both the curved part and the diameter. Of course that will give a different answer.

If the semicircle to be formed is a closed figure, then

%28pi%2F2%29d%2Bd=1
%28%28pi%2F2%29%2B1%29d=1
d+=+1%2F%28%28pi%2F2%29%2B1%29

Note that the calculations shown for both interpretations are in meters; since the question asks for an answer in centimeters, you need to do a simple conversion of units.