Final answer:
The surface area of a cylinder with a base radius of 2' and a height of 14' is (8π + 56π) square feet, calculated using the formula A = 2πr² + 2πrh. The correct answer is (a) (8π + 56π).
Step-by-step explanation:
To find the surface area of a cylinder, we use the formula A = 2πr² + 2πrh, where r is the radius of the base and h is the height of the cylinder. We are given that the base radius r is 2 feet and the height h is 14 feet. Substituting these values into the formula, we get:
A = 2π(2²) + 2π(2)(14)
A = 2π(4) + 2π(28)
A = 8π + 56π
The surface area of the cylinder is therefore (8π + 56π) or 64π square feet.
Thus, the correct choice is (a) (8π + 56π).