Final answer:
The approximate area of the curved sides of each storage tank at the refinery to be painted is 2,287 square feet, calculated using the lateral surface area formula for a cylinder. option A is correct answer.
Step-by-step explanation:
To find the approximate area of each tank that needs to be painted, we will calculate the surface area of a cylinder without the top and bottom. Since the problem only asks about the curved sides, we won't include the areas of the circles at the ends of the cylinder.
First, we need to know the diameter and height of the cylinder to calculate the lateral surface area. Given that the tank has a diameter of 28 feet and a height of 26 feet, the radius (which is half of the diameter) is thus 14 feet.
The formula for the lateral surface area of a cylinder (curved surface area) is:
A = 2πrh
Where:
A is the lateral surface area,
π (pi) is approximately 3.14159265,
r is the radius of the base, and
h is the height of the cylinder.
By substituting the known values into the formula, we have:
A = 2 × 3.14159265 × 14 ft × 26 ft
A = 2 × 3.14159265 × 364 ft
A ≈ 2 × 3.14 × 364 ft
A ≈ 2287 ft2
The approximate area of each tank that will be painted is 2,287 ft2.