Answer: A. SA = 2π(2.8)² + 2.8π(4.2) square feet
To understand this calculation, let's break it down step by step:
1. The formula for the surface area of a cylinder is SA = 2πr² + 2πrh, where r is the radius of the base and h is the height of the cylinder.
2. In the given question, the diameter of the cylinder is labeled as 2.8 feet. The radius of the base can be calculated by dividing the diameter by 2: radius = 2.8/2 = 1.4 feet.
3. The first part of the equation, 2π(2.8)², calculates the surface area of the two circular bases of the cylinder. To find the area of a circle, we use the formula A = πr². Plugging in the radius of 1.4 feet, we get 2π(1.4)².
4. The second part of the equation, 2.8π(4.2), calculates the surface area of the curved side of the cylinder. This is found by multiplying the circumference of the base (2πr) by the height of the cylinder (4.2 feet).
5. By adding the two parts together, we get the total surface area of the cylinder in square feet.
Therefore, option A, SA = 2π(2.8)² + 2.8π(4.2) square feet, is the correct method to calculate the surface area of the given cylinder.