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To find the surface area of a cylinder, you need to find the area of the two circular bases and the lateral surface area.
First, let's find the area of the two circular bases:
Area of a circle = ฯr^2
Area of the top base = ฯ(3 in)^2 = 9ฯ sq in
Area of the bottom base = ฯ(3 in)^2 = 9ฯ sq in
Now, let's find the lateral surface area:
Lateral surface area = 2ฯrh
Lateral surface area = 2ฯ(3 in)(6 in) = 36ฯ sq in
Now, calculate the total surface area by adding the areas of the two bases and the lateral surface area:
Total surface area = 9ฯ + 9ฯ + 36ฯ = 54ฯ sq in
Now, substitute 3.14 for ฯ:
Total surface area โ 54 * 3.14 โ 169.56 sq in
Therefore, the approximate surface area of the cylinder is approximately 169.56 square inches.