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

1. Identify the radius of the circular base of the cone. Let’s call this radius r.
2. Identify the height of the cone. Let’s call this height h.
3. Calculate the slant height of the cone using the Pythagorean theorem. The slant height is the distance from the tip of the cone to any point on the edge of the circular base. The formula for the slant height is:

   l = sqrt(r^2 + h^2)

4. Calculate the area of the circular base of the cone using the formula:

   A = pi * r^2

5. Calculate the lateral surface area of the cone using the formula:

   L = pi * r * l

6. Add the area of the circular base and the lateral surface area to get the total surface area of the cone:

   T = A + L

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

T = pi * r^2 + pi * r * sqrt(r^2 + h^2)

where:

• T is the total surface area of the cone
• r is the radius of the circular base of the cone
• h is the height of the cone
• pi is the mathematical constant pi (approximately 3.14159)
• sqrt() represents the square root function.

I hope this helps!