You are in charge of ordering the concrete for a basement wall concrete pour. The wall forms are all set up and ready. The wall around the basement is 10 inches thick. The interior finished dimension of the basement is 120 feet 5 inches by 86 feet 4-1/2 inches and fourteen (14') feet tall. What is the exact quantity of concrete in cubic yards (CY) to order plus three (3%) per cent added for spilled concrete.

: To calculate the exact quantity of concrete needed, we first need to determine the volume of the wall. We do this by calculating the volume of the outer dimensions of the wall and then subtracting the volume of the inner (finished) dimensions.

1. Calculate the outer dimensions of the wall. Given that the thickness of the wall is 10 inches, we need to add this thickness to all four sides of the interior dimensions to get the outer dimensions.

The interior finished dimension is 120 feet 5 inches by 86 feet 4-1/2 inches. - Add 10 inches (which is 0.8333 feet) to both the length and width to get the outer dimensions. - Calculate it in feet for ease of computation.

Length (outer): 120 feet 5 inches + (10 inches × 2) Width (outer): 86 feet 4-1/2 inches + (10 inches × 2)

First, convert the inches to feet: 5 inches = 5/12 = 0.4167 feet 4.5 inches = 4.5/12 = 0.375 feet

Then, add the thickness in feet to the length and width: Length (outer) = 120.4167 feet + 1.6666 feet = 122.0833 feet Width (outer) = 86.375 feet + 1.6666 feet = 88.0416 feet

2. Calculate the volume of concrete for the outer wall: Volume (outer) = Length (outer) × Width (outer) × Height Volume (outer) = 122.0833 ft × 88.0416 ft × 14 ft

3. Calculate the volume of the inner wall space to subtract from the outer wall volume. The interior finished dimensions are given as 120 feet 5 inches by 86 feet 4-1/2 inches. Length (inner) = 120 feet + (5 inches in feet) Width (inner) = 86 feet + (4.5 inches in feet) Length (inner) = 120.4167 feet Width (inner) = 86.375 feet

Volume (inner) = Length (inner) × Width (inner) × Height Volume (inner) = 120.4167 ft × 86.375 ft × 14 ft

4. Find the concrete volume needed for the wall by subtracting the inner volume from the outer volume: Concrete Volume = Volume (outer) - Volume (inner)

5. Finally, add 3% to account for spillage: Total Concrete Volume = Concrete Volume + (Concrete Volume × 0.03)

6. Convert the Total Concrete Volume from cubic feet to cubic yards by dividing by 27, since there are 27 cubic feet in a cubic yard: Total Concrete Volume (CY) = Total Concrete Volume (cubic feet) / 27

Now you just need to plug in the values to get the Total Concrete Volume in cubic yards and that's the quantity you will order.

Extra: Understanding how to calculate volumes for construction is critical. As a construction project progresses, contractors need to know the volumes of the materials required to coordinate purchases and ensure the project moves forward without delays.

Cubic yards (CY) is a standard unit of measure used in construction for materials like concrete, because concrete trucks are often rated in cubic yards. In the construction world, knowing the exact amount of materials such as concrete is crucial not only to prevent running short on a project but also to avoid ordering too much, which would be wasteful and costly.

Percentage calculations like adding 3% for spillage are standard practice as they account for errors, miscalculations, or waste that inevitably happens during construction.

Having an understanding of how these calculations are done can be very useful for anyone interested in construction, engineering, or architecture. Moreover, a strong grasp of basic arithmetic and geometry can help students to solve real-world problems like this one.