Question

1. find the radius of a circle so that its area and circumference have the same value.

Explanation:

Step1: Recall area and circumference formulas

The area formula of a circle is $A = \pi r^{2}$, and the circumference formula is $C=2\pi r$.

Step2: Set area equal to circumference

Set $\pi r^{2}=2\pi r$.

Step3: Solve the equation

First, move all terms to one - side: $\pi r^{2}-2\pi r = 0$. Factor out $\pi r$: $\pi r(r - 2)=0$. Then, we have two solutions from the zero - product property. $\pi r=0$ gives $r = 0$ (but a circle with radius 0 is a degenerate case and we ignore it), and $r - 2=0$ gives $r=2$.

Answer:

$2$