To find the surface area of a cylinder, we need to calculate the area of the two bases and the lateral surface area, and then sum them up.
Let's start with the bases. The base of a cylinder is a circle, and the formula to find the area of a circle is A = πr², where A is the area and r is the radius.
Given that the diameter of the cylinder is 12 inches, we can calculate the radius by dividing the diameter by 2: r = 12 / 2 = 6 inches.
Now, we can substitute the radius into the formula to find the area of one base: A1 = 3.14 * (6)² = 3.14 * 36 = 113.04 square inches.
Since a cylinder has two bases, the total area of the bases is: A_base = 2 * A1 = 2 * 113.04 = 226.08 square inches.
Next, let's calculate the lateral surface area. The lateral surface area of a cylinder can be found using the formula A_lateral = 2Ï€rh, where h is the height of the cylinder.
Substituting the given values, we get: A_lateral = 2 * 3.14 * 6 * 10 = 376.8 square inches.
Finally, we can find the total surface area by adding the area of the bases and the lateral surface area: A_total = A_base + A_lateral = 226.08 + 376.8 = 602.88 square inches.
Therefore, the surface area of the cylinder is approximately 602.88 square inches.