the step-by-step process for calculating the total surface area of a cylinder:

1. Identify the radius of the circular base of the cylinder. Let’s call this radius r.
2. Identify the height of the cylinder. Let’s call this height h.
3. Calculate the lateral surface area of the cylinder. This is the area of the curved surface of the cylinder. The formula for the lateral surface area is:

   L = 2 * pi * r * h

4. Calculate the area of the circular base of the cylinder. The formula for the area of a circle is:

   A = pi * r^2

   Since the cylinder has two circular bases, the total base area is:

   B = 2 * A = 2 * pi * r^2

5. Add the lateral surface area and the base area to get the total surface area of the cylinder:

   T = L + B = 2 * pi * r * h + 2 * pi * r^2

So, the complete formula for calculating the total surface area of a cylinder is:

T = 2 * pi * r * h + 2 * pi * r^2

where:

• T is the total surface area of the cylinder
• r is the radius of the circular base of the cylinder
• h is the height of the cylinder
• pi is the mathematical constant pi (approximately 3.14159)

I hope this helps!