The circumference of the base of the cylinder is 1. The lateral surface area is 2. Find the height of the cylinder.

We need to determine the height of the cylinder.

To do this, we can use the formula to find the area of the lateral surface of a cylinder.

We know that if we unfold the lateral surface of the cylinder, we will get a rectangle. Consequently, the area in this case will be found as length by width. In our case, the circumference is the height. That is, we get:

S = l * h

Let us express the height from this formula:

h = S * l

According to the condition of the problem:

h = 2/1 = 2

That is, the cylinder height is 2.