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

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2 Answers

3 votes
The formula for circumference of a circle:

C=2 \pi r

The formula for area of a circle:

A=\pi r^2
r - radius

The circumference is equal to the area.

C=A \\ 2 \pi r=\pi r^2 \ \ \ |/ \pi r, \ r>0 \\ 2=r \\ r=2

The diameter is two times the radius.

d=2r=2 * 2=4 \\ \\ \boxed{d=4}
User Dr Phil
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3 votes

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.


User Ashkulz
by
7.6k points

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