Question

Challenge The Travers are adding a new room to their house. The room will be a cube with volume 4,913 ft³. They are going to put in hardwood floors, and the contractor charges $10 per square foot. How much will the hardwood floors cost?​

Answer 1

To calculate the cost of the hardwood floors, we need to determine the surface area of the cube. Since it's a cube, all sides have the same length.

The volume of a cube is given by the formula:

Volume = side length³

Given that the volume of the cube is 4,913 ft³, we can solve for the side length:

4,913 ft³ = side length³

Taking the cube root of both sides, we get:

side length = ∛4,913 ft³ ≈ 17.47 ft

Now, we can calculate the surface area of the cube:

Surface Area = 6 * (side length)²

Surface Area = 6 * (17.47 ft)² ≈ 1,935.20 ft²

Finally, we can calculate the cost of the hardwood floors by multiplying the surface area by the cost per square foot:

Cost = Surface Area * Cost per square foot

Cost = 1,935.20 ft² * $10/ft² ≈ $19,352

Therefore, the hardwood floors will cost approximately $19,352.