In a straight circular cylinder, the axial section is square, its lateral surface is 80π cm2.

In a straight circular cylinder, the axial section is square, its lateral surface is 80π cm2. Find the complete surface of the cylinder.

To solve this problem for us, we need to perform the following actions:
Let us denote the variables: S is the total surface of the cylinder, r is the radius of the circumference of the base of the cylinder, h is the height of the cylinder.
Then by the formula: S₁ = 2πrh lateral surface.
H = 2r axial section, square.
Substitute h in the formula.
S₁ = 4 * π * r² = 80 * π.
From the tower formula we find: r² = 20.
Let’s find the area of the base: S₂ = π * r² = 20 * π.
The total area is then: S = S₁ + 2 * S₂ = 80 * π + 2 * 20 * π = 120 * π.
As a result of the actions taken, we get the answer to the problem: 120π.