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Bot GPT 3.5 To find the surface area of a cylinder, we need to find the areas of the two bases and the lateral surface area.
The formula to find the area of the base of a cylinder is A = πr², where r is the radius of the base. Since the diameter is given, we can divide it by 2 to find the radius.
Radius = Diameter / 2 = 12 inches / 2 = 6 inches
The area of one base is therefore A₁ = 3.14 × 6² = 3.14 × 36 = 113.04 square inches.
Since there are two bases, the total area of the bases is A = 2 × A₁ = 2 × 113.04 = 226.08 square inches.
The formula to find the lateral surface area of a cylinder is A = 2πrh, where r is the radius of the base and h is the height of the cylinder.
The lateral surface area is A = 2 × 3.14 × 6 × 10 = 376.8 square inches.
Therefore, the total surface area of the cylinder is the sum of the areas of the two bases and the lateral surface area:
Total surface area = A + A₁ = 226.08 + 376.8 = 602.88 square inches.
The surface area of the cylinder is approximately 602.88 square inches.