Find the height of the cylinder if its base area is 1 and the side surface area is √П

The area of the cylinder base can be determined by the formula: Sbase = π (d ^ 2) / 4, where d is the diameter of the cylinder base. We find d: πd ^ 2 = 4Ssn, d ^ 2 = 4Ssn / π, d = √ (4Ssn / π). By the condition Sbase = 1, so d = √ (4 / π) = 2 / √π.
The area of the lateral surface of the cylinder is defined as the product of the height of the cylinder and the circumference of the base: Side = h * πd. Hence, h = Sside / πd, substituting the value found above for d and the value given by the condition Sside = √π, we obtain:
h = √π / (π * 2 / √π) = 1/2.