Final answer:
To cover the surface area of a cube with a volume of 2197 cubic meters, we find that each side of the cube is 13 meters long. The total surface area is 1014 square meters, and with each can of paint covering 40 square meters, we need 26 cans of paint after rounding up.
Step-by-step explanation:
To determine how many cans of paint are necessary to cover the surface area of a cube with a volume of 2197 cubic meters, we need to follow a series of steps. First, we find the length of one side of the cube by taking the cube root of the volume. The cube root of 2197 cubic meters is 13 meters, indicating that each side of the cube is 13 meters long.
The surface area (SA) of a cube is calculated by the formula SA = 6 × s², where 's' is the length of a side of the cube. Substituting 13 meters for 's', we calculate the surface area as SA = 6 × (13²) = 6 × 169 = 1014 square meters.
Given that each can of paint covers about 40 square meters, the number of cans required is the surface area divided by the coverage of one can. Therefore, 1014 square meters ÷ 40 square meters per can equals approximately 25.35 cans. Since we cannot purchase a fraction of a can, we round up to the nearest whole number, resulting in 26 cans of paint required to paint the surface of the cube.