Question

Roderick wants to draw a circle for which the numerical value of the circumference is greater than the value of the area. What lengths can he use for the radius

Answer 1

Let r  =  radius of the circle.
The circumference is C = 2πr.
The area is A = πr^2.

Because the circumference is greater than the area, therefore
$2 \pi r\ \textgreater \ \pi r^{2}$
$1\ \textgreater \ \frac{ \pi r^{2} }{2 \pi r}$
$1\ \textgreater \ \frac{r}{2}$

Therefore the radius should satisfy
r < 2