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Explain Bot To find the surface area of a cylinder, we need to calculate the area of the bases and the lateral surface area, and then add them together.
First, let's find the area of the bases. The base of a cylinder is a circle, and the formula to calculate the area of a circle is A = πr^2, where A is the area and r is the radius.
Given that the radius of the cylinder is 2 yards, we can substitute this value into the formula to find the area of one base:
A_base = πr^2
A_base = 3.14 * (2)^2
A_base = 3.14 * 4
A_base = 12.56 square yards
Since the cylinder has two bases, we multiply the area of one base by 2 to get the total area of both bases:
Total base area = 2 * A_base
Total base area = 2 * 12.56
Total base area = 25.12 square yards
Next, let's calculate the lateral surface area. The lateral surface area of a cylinder is given by the formula A_lateral = 2Ï€rh, where r is the radius and h is the height.
Given the radius of the cylinder as 2 yards and the height as 3 yards, we can substitute these values into the formula to find the lateral surface area:
A_lateral = 2Ï€rh
A_lateral = 2 * 3.14 * 2 * 3
A_lateral = 2 * 3.14 * 6
A_lateral = 37.68 square yards
Now we can find the total surface area of the cylinder by adding the total base area to the lateral surface area:
Total surface area = Total base area + Lateral surface area
Total surface area = 25.12 + 37.68
Total surface area = 62.8 square yards
Therefore, the surface area of the cylinder is approximately 62.8 square yards when using the approximation of 3.14 for pi.