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

The correct option is 4 unit.

To find the diameter of the circle, we begin by writing down the mathematical formulas for the area and the circumference of a circle.

Let the radius of the circle be represented by r, and the diameter of the circle be represented by d.

The formula for the area (A) of a circle is:
$$A=\pi r^2$$
The formula for the circumference (C) of a circle is:
$$C=2\pi r$$

According to the given problem, the area of the circle is numerically equal to its circumference. Therefore, we can set the two formulas equal to each other:
$$\pi r^2=2\pi r$$

To solve for the radius r, we can divide both sides of the equation by $\pi r$ (assuming the radius r is non-zero):
$$\frac{\pi r^2}{\pi r}=\frac{2\pi r}{\pi r}$$
This simplifies directly to:
$$r=2\text{units}$$

Now that we have the radius, we can find the diameter (d) of the circle. The diameter is defined as twice the radius:
$$d=2r$$
Substituting the value of the radius $r=2$ into the formula:
$$d=2\times 2=4\text{units}$$

Thus, the diameter of the circle is 4 unit.