The area of a circle is numerically equal to its circumference. Find the diameter of the circle.

Question

Accepted Answer

The area of a circle is given by $$ \pi r^2 $$, and the circumference is $$ 2\pi r $$. According to the problem, these two are equal:

$$
\pi r^2 = 2\pi r
$$

Divide both sides by $$ \pi $$ (assuming $$ \pi 
eq 0 $$):

$$
r^2 = 2r
$$

Rearrange the equation:

$$
r^2 - 2r = 0
$$

Factorize:

$$
r(r - 2) = 0
$$

This gives two solutions: $$ r = 0 $$ or $$ r = 2 $$. Since the radius cannot be zero, $$ r = 2 $$.

The diameter $$ d $$ of a circle is twice the radius:

$$
d = 2r = 2 	imes 2 = 4 \, 	ext{units}.
$$

Thus, the diameter of the circle is **4 units**.

Answer

Answer

Answer