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Find the diameter of the circle that has a circumference equal to its area.

2
4
8
10

Sagot :

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The formula for circumference of a circle:
[tex]C=2 \pi r[/tex]

The formula for area of a circle:
[tex]A=\pi r^2[/tex]
r - radius

The circumference is equal to the area.
[tex]C=A \\ 2 \pi r=\pi r^2 \ \ \ |\div \pi r, \ r>0 \\ 2=r \\ r=2[/tex]

The diameter is two times the radius.
[tex]d=2r=2 \times 2=4 \\ \\ \boxed{d=4}[/tex]
AL2006

Circumference may have the same numerical magnitude as area, but they will never be "equal".  Circumference is a length or distance, and area is an area.
So they can never have the same units, and quantities can't be equal without
the same units.

You might say that   π D (circumference) = π (D/2)²  (area) .

Then  D = (D/2)²

           D = D² / 4

           1 = D / 4

           D = 4 .

But this is no more than a parlor trick.  In order to do it, you need to
ignore units completely, and that's unacceptable in math.


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