Find the surface area of a conical grain storage tank that has a height of 42 meters and a diameter of 20 meters. Round the answer to the nearest square meter.

3,028m2
3,971m2
1,357m2
1,671m2

To find the surface area of a conical tank, we need to calculate the curved surface area and the base area of the tank separately and then add them together.

First, let's find the curved surface area of the cone. The formula for the curved surface area of a cone is π × r × s, where r is the radius of the base and s is the slant height of the cone. To find the slant height (s), we can use the Pythagorean theorem. The slant height, s, is the square root of (h^2 + r^2), where h is the height and r is the radius.

Given:
Height (h) = 42 meters
Diameter = 20 meters (radius = diameter/2 = 10 meters)

First, let's find the slant height (s):
s = √(h^2 + r^2)
s = √(42^2 + 10^2)
s = √(1764 + 100)
s = √1864
s ≈ 43.13 meters (rounded to two decimal places)

Next, let's find the curved surface area:
Curved Surface Area = π × r × s
Curved Surface Area = π × 10 meters × 43.13 meters
Curved Surface Area ≈ 1,357.16 square meters (rounded to two decimal places)

Now, let's find the base area of the cone. The base of a cone is a circle, so the base area is given by the formula π × r^2.

Base Area = π × r^2
Base Area = π × 10 meters^2
Base Area ≈ 314.16 square meters (rounded to two decimal places)

Finally, we can calculate the total surface area by adding the curved surface area and the base area:
Total Surface Area = Curved Surface Area + Base Area
Total Surface Area ≈ 1,357.16 square meters + 314.16 square meters
Total Surface Area ≈ 1,671.32 square meters (rounded to two decimal places)

Therefore, the correct answer is approximately 1,671m2 (rounded to the nearest square meter).