Final answer:
The surface area of a cylinder with a base diameter of 6 yards and a height of 14 yards is approximately 376.8 square yards, with the closest match from the options provided being 376 square yards (Option A).
Step-by-step explanation:
The surface area of a cylinder can be found using the formula: Surface Area = 2πr(h + r), where r is the radius of the base and h is the height of the cylinder. Given that the base diameter of the cylinder is 6 yards, the radius (r) would be half of that, which is 3 yards. Plugging the values into the formula:
Surface Area = 2π(3)(14 + 3)
Surface Area = 2π(3)(17)
Surface Area = 2π * 51
Surface Area = 102π
Since π is approximately 3.14, we can then multiply 102 by 3.14 to get:
Surface Area ≈ 320.28 square yards
However, since this doesn't match any of the answer options provided in the question, we may need to assume the question meant the total surface area, which includes both the top and bottom circles of the cylinder. Thus:
Total Surface Area = (2 πr²) + (2πrh)
Total Surface Area = (2π(3)²) + (2π(3)(14))
Total Surface Area = (2π(9)) + (2π(3)(14))
Total Surface Area = (18π) + (84π)
Total Surface Area = 102π
Total Surface Area ≈ 320.28 square yards (lateral surface) + 56.52 square yards (top and bottom circles)
Total Surface Area ≈ 320.28 + 56.52
Total Surface Area ≈ 376.8 square yards
Therefore, the closest answer choice is A) 376 square yards.