What is the surface area of a conical grain storage tank that has a height of 54 meters and a diameter of 18 meters

  81π(1+√37) m² ≈ 1802.3 m²

Step-by-step explanation:

The total surface area will be the sum of the lateral area and the area of the base. In order to find the lateral area, we need to know the slant height of the tank.

The slant height is the hypotenuse of a right triangle that has one leg equal to the height of the bin, and the other leg equal to its radius. The radius is half the diameter, so is 9 m.

  s² = h² +r²

  s² = 54² +9² = 9²·37 . . . . fill in the known values

  s = 9√37 . . . . . . . . . . . . square root

The lateral area is ...

  LA = πrs

  LA = π(9 m)(9√37 m) = 81√37π m²

The base area is ...

  B = πr²

  B = π(9 m)² = 81π m²

The total surface area of the tank is ...

  SA = LA +B

  SA = (81√37π m²) +(81π m²) = 81π(1+√37) m² ≈ 1802.3 m²