Whitewashing Cost Calculation For A 20m By 120dm Building Facade
Understanding the Project Scope
Alright guys, let's dive into a practical geometry problem! We've got a building facade that needs a fresh coat of whitewash, and we need to figure out the total cost. This involves some basic area calculations and cost estimation. To kick things off, the main objective here is calculating whitewashing costs, and it requires us to determine the total surface area of the facade before figuring out the total expenditure. The building in question stretches 20 meters in length and soars 120 decimeters in height. Now, before we start crunching numbers, it's super important to make sure we're all on the same page with our units. We're given the length in meters and the height in decimeters, but to make our calculations smooth and accurate, we need to convert everything into the same unit. Since the cost of whitewashing is given per square meter (m²), let’s convert the height from decimeters to meters. There are 10 decimeters in a meter, so 120 decimeters is equal to 12 meters (120 dm ÷ 10 = 12 m). Now we're talking the same language! The facade is essentially a rectangle, and to find its area, we multiply the length by the height. So, we have a rectangle that is 20 meters long and 12 meters high. The area of this rectangle will give us the total surface area that needs whitewashing. The formula for the area of a rectangle is Area = Length × Height. Once we have the total area in square meters, we can then multiply it by the cost per square meter to find the total cost of the whitewashing project. This is where the 180 rubles per square meter comes into play. We'll use this figure to determine the overall expense. Estimating total costs for the whitewashing project involves these sequential steps – unit conversion, area calculation, and multiplication by the per-unit cost. Doing this methodically helps us arrive at a precise and trustworthy estimate, making sure no factors are missed. Let's get our calculators ready and figure out how much this whitewashing project will cost!
Calculating the Facade Area
Now, let's move on to calculating the facade area. With our units aligned—both length and height now conveniently in meters—we can accurately find the space we plan to whitewash. This part is actually pretty straightforward. We know the facade is rectangular, and we've already got the dimensions sorted out: 20 meters in length and 12 meters in height. Remember, the formula to calculate the area of a rectangle is Area = Length × Height. So, to find the area of our facade, we just need to multiply these two numbers together. This calculation gives us the total surface area that will be covered with whitewash. Understanding how to calculate the area of the facade is essential not just for this project but for a bunch of other practical applications too. Figuring out areas helps with everything from planning renovations to estimating materials for construction. By calculating the area of the rectangular facade, we can precisely define the scope of the project and how much resources it'll demand. Multiplying the length (20 meters) by the height (12 meters) will give us the total area in square meters. This number is crucial because it directly affects the amount of whitewash needed and, consequently, the total cost. Once we have this figure, we're one step closer to our final answer. So, let’s crunch these numbers and see what we get. This step is key to ensuring we accurately estimate the materials and costs involved in the whitewashing project, making sure we're both efficient and cost-effective in our approach. With the area calculated, we'll be all set to tackle the final cost calculation, turning a theoretical problem into a real-world budget. Stay tuned, because next, we'll use this area to determine the total cost of the project!
Determining the Total Whitewashing Cost
Alright, guys, we're in the home stretch! We've figured out the facade area, and now it’s time to determine the total cost for whitewashing. We know the area that needs to be covered, and we also know the cost per square meter for the whitewash. The cost is 180 rubles per square meter. To find the total cost, we simply multiply the total area of the facade by the cost per square meter. This will give us the final figure, showing us exactly how much the entire project will cost. This step is all about determining total costs, and it’s where all our previous calculations come together. Accurate cost estimation is super important for planning any project, whether it’s a small DIY task or a large-scale renovation. By multiplying the area by the cost per square meter, we ensure that we're accounting for every bit of the surface that needs to be covered, giving us a precise and realistic budget. Let's use the area we calculated earlier and multiply it by 180 rubles. The resulting number will be the total amount we need to spend on whitewashing the entire facade. This calculation not only gives us the financial figure but also helps in decision-making. For example, if the total cost exceeds the budget, we might need to explore alternative materials or methods. By understanding how per-unit costs affect the overall project expenses, we can make informed choices and manage resources effectively. So, let’s grab that area figure, do the multiplication, and reveal the total cost. This is the number we’ve been working towards, and it represents the final piece of the puzzle in our whitewashing project. Once we have this, we'll have a complete picture of the project's financial aspect. With the total cost determined, we can move forward with confidence, knowing we’ve planned our budget accurately. Let's get those calculations done and see what the total cost is!
Final Calculation and Total Cost
Okay, let’s wrap this up with the final calculation! We’ve broken down the problem step by step, and now it’s time to put it all together and get our answer. Earlier, we calculated the area of the facade by multiplying the length (20 meters) by the height (12 meters). This gave us an area of 240 square meters (20 m × 12 m = 240 m²). Now that we have the total area, we need to multiply this by the cost per square meter to find the total cost of the whitewashing project. The cost per square meter is 180 rubles. So, we multiply the total area (240 square meters) by the cost per square meter (180 rubles) to get the total cost: 240 m² × 180 rubles/m² = 43,200 rubles. Therefore, the total cost to whitewash the facade of the building is 43,200 rubles. The final calculation shows us exactly how much the project will cost, which is crucial for budgeting and planning. This entire process highlights the importance of breaking down a problem into smaller, manageable steps. By converting units, calculating the area, and then multiplying by the cost per unit, we arrived at an accurate and reliable estimate. Understanding each step not only makes the problem easier to solve but also provides valuable insights into real-world applications of geometry and cost estimation. We started with a seemingly complex problem and, through methodical steps, turned it into a clear, concise answer. Now we know that the total cost for the whitewashing project is 43,200 rubles. This figure allows us to make informed decisions and manage our resources effectively. This exercise not only solves a specific problem but also reinforces the broader skills of problem-solving, unit conversion, area calculation, and cost estimation—all essential in various fields and everyday situations. So, there you have it! The facade can be whitewashed for 43,200 rubles. Let’s consider this task accomplished and move on to the next challenge!
Conclusion
So, guys, we've successfully calculated the total cost for whitewashing the building facade! We started by understanding the dimensions of the facade, converted the units to ensure consistency, calculated the total area, and finally, determined the total cost by multiplying the area by the cost per square meter. The final figure came out to be 43,200 rubles. This exercise demonstrates a practical application of geometry and basic arithmetic in a real-world scenario. Throughout this process, we've seen how important it is to break down a complex problem into smaller, more manageable steps. By approaching the problem methodically, we were able to navigate through each calculation with accuracy and confidence. Summarizing the total costs and understanding the process helps us appreciate how math concepts apply to everyday situations. Whether you're planning a home renovation project, estimating materials for a construction job, or simply trying to figure out the cost of a service, the principles we've used here are universally applicable. We've not only found a solution to a specific problem but also reinforced valuable skills in problem-solving, unit conversion, area calculation, and cost estimation. These skills are crucial in various fields and can help us make informed decisions in our daily lives. The key takeaways from this calculation include the importance of accuracy, the value of breaking down problems, and the practical applications of mathematical concepts. We've shown that even a seemingly complex question can be answered effectively with a step-by-step approach. This exercise also highlights the significance of cost estimation in project planning. By accurately calculating the total cost, we can ensure that our budget is realistic and that we can proceed with the project confidently. So, congratulations, guys, on tackling this problem together! We've successfully calculated the whitewashing cost, and we've learned some valuable lessons along the way. This exercise shows us that with a clear approach and a bit of math, we can tackle a variety of real-world challenges effectively.
