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To calculate the base surface area, you need to compute the area of a circle with the radius r. But remember that every cylinder has two bases! Thus, you need to multiply it by two:
Base area = 2 × π × r²
Estimation of the lateral surface area is even easier. Because the area of a rectangle is the product of its sides, we can write that:
Lateral area = (2 × π × r) × h
where 2 × π × r is the circumference of the base circle, and h is the height of a cylinder.
Finally, the total surface area of the cylinder formula is simply the sum of the base surface area and the lateral surface area:
Total area = Base area + Lateral area
or Total area = 2 × π × r² + (2 × π × r) × h
or Total area = 2 × π × r × (r + h)