The area of a circle and a square

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Question from Richard, a parent:

I cannot understand why if you have a perimeter say of 4 units as the circumference of
a circle then you reshape it into a square you lose very approximately some 20% of its
volume but the perimeter length stays the same.
Can you please explain this to me as to why the volume decreases.

Hi Richard,

I think you mean area not volume.

I took a unit to be 10 centimeters and cut a length of wire 40 centimeters long. I then bent the wire into a circle, or as close to a circle as I could.

circle

Next I cut a square of side length 10 centimeters from some paper and placed the square over the circle.

circle and square

It is clear that the area inside the circle is quite a bit larger than the area inside the square.

I hope this helps,
Penny

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