Final answer:
To calculate the cost of the hardwood floors for the cubic room, find the cube root of the room's volume to get the length of a side, calculate the square footage of the floor, and then multiply by the cost per square foot. The total cost is $1,280.
Step-by-step explanation:
The question involves calculating the cost of hardwood floors for a cubic room. First, we need to determine the length of one side of the cube which is the cube root of the volume.
Since the volume of the room is 4,096 cubic feet, the cube root of 4,096 is 16 feet. This means each side of the room is 16 feet. The area of the floor, which is one side of the cube, would be 16 feet by 16 feet, giving us 256 square feet.
Next, we need to calculate the cost of the hardwood flooring. The contractor charges $5 per square foot. Therefore, to find the total cost, we multiply the area of the floor by the cost per square foot:
256 square feet × $5/square foot = $1,280
Thus, the cost of the hardwood floors for the new room will be $1,280.