Answer :
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]
[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]
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.
