Question

Can the area of a circle ever equal the circumference of a circle? Explain.

Answer 1

YES. it can

Circumference = pi*diameter OR 2*radius*pi (since the diameter is 2*radius)
Area = pi*radius^2 (squared)

so set them equal to each other
2*pi*r = pi*r^2

divide both sides by pi*r
2 = r

so when the radius is 2, the circumference is 2*pi*r = 2*pi*2 = 4*pi
and the area = (r^2)*pi= (2^2)*pi = 4*pi

Answer 2

wow... I thought 1 was a measurement of area and the other was a linear measurement...

so how does 4pi inches^2 = 4 pi inches...?

Answer 3

\[\pi r^2=2\pi r,\pi r^2-2 \pi r=0,\pi r \left( r-2 \right)=0,\]
either r=0
or r=2