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The formula to calculate the total surface area of a cylinder is given by 2πr(h + r), where r is the radius of the base and h is the height of the cylinder.
Given that the radius of the cylinder is 5 cm and the height is 20 cm, we can plug these values into the formula:
Total surface area = 2 * 3.14 * 5(20 + 5)
Total surface area = 2 * 3.14 * 5(25)
Total surface area = 2 * 3.14 * 125
Total surface area = 6.28 * 125
Total surface area = 785 square centimeters
Therefore, the total surface area of the cylinder is 785 square centimeters.