To find the surface area of a cylinder, we need to calculate the sum of the lateral surface area and the two circular bases.
1. First, let's find the radius of the cylinder since the diameter is given as one-third of the height. The diameter is 1/3 of the height, so the radius (r) is half of the diameter, which is 1/6 of the height. Given the height is 42 meters, the radius (r) is 42 / 6 = 7 meters.
2. The lateral surface area of a cylinder is given by the formula: 2πrh, where r is the radius and h is the height. Substituting the values we found, the lateral surface area is 2 * π * 7 * 42 = 588π square meters.
3. The area of each circular base of the cylinder is πr^2. Substituting the radius (7 meters) into the formula, the area of each base is π * 7^2 = 49π square meters. Since there are two bases, the total area of the bases is 2 * 49π = 98π square meters.
4. Finally, the total surface area of the cylinder is the sum of the lateral surface area and the two base areas. Therefore, the total surface area is 588π + 98π = 686π square meters.
Therefore, the correct answer is:
B. 686π m²
