The total surface area of a cylinder can be calculated by finding the sum of the areas of the two circular bases and the lateral surface area.
To start, let's find the area of each circular base. The formula for the area of a circle is A = πr², where A is the area and r is the radius. The radius of the base is half of the diameter, so in this case, the radius is 2 cm ÷ 2 = 1 cm.
Using this information, we can calculate the area of each circular base as follows:
A = π(1 cm)² = π(1 cm)(1 cm) = π cm²
Since there are two circular bases, the total area of the bases is 2π cm².
Next, let's find the lateral surface area of the cylinder. The lateral surface area of a cylinder is given by the formula A = 2πrh, where A is the area, π is a constant approximately equal to 3.14, r is the radius, and h is the height.
In this case, the radius is 1 cm and the height is 2 cm. Plugging these values into the formula, we get:
A = 2π(1 cm)(2 cm) = 4π cm²
Now, we can find the total surface area of the cylinder by adding the areas of the bases and the lateral surface area:
Total Surface Area = 2π cm² + 4π cm² = 6π cm²
To find the numerical value of the total surface area, we can approximate π as 3.14:
Total Surface Area ≈ 6(3.14) cm² ≈ 18.84 cm²
Therefore, the total surface area of the cylinder is approximately 18.84 square centimeters.