Painting A Room: Area & Cost Calculation

by TextBrain Team 41 views

Hey guys! Ever wondered how much paint you need for a room makeover or how to calculate the cost? Let's break down a classic math problem involving room dimensions, surface area, and painting costs. We'll tackle this step-by-step, making it super easy to understand. So, grab your calculators, and let's get started!

Understanding the Problem

First, let’s restate the problem clearly. We have a room with the following dimensions:

  • Length: 10 meters
  • Breadth: 6 meters
  • Height: 15 meters

The task is twofold: calculate the total surface area of the walls and ceiling that need to be painted and then determine the cost of painting this area at a rate of ₹5 per square meter. This kind of problem is a practical application of geometry, helping us understand how to apply area calculations in real-world scenarios. We'll use basic formulas for the area of rectangles and then apply this knowledge to find the total cost.

Calculating the Surface Area

The heart of this problem lies in calculating the surface area. We need to consider the walls and the ceiling separately, then add them up. Let's break it down:

1. Walls

The room has four walls. Two of these walls will have the same area (length × height), and the other two will also have the same area (breadth × height). So, let's calculate these areas:

  • Wall 1 & 3 Area (Length × Height): 10 m × 15 m = 150 m²
  • Since there are two such walls, their combined area is 150 m² × 2 = 300 m².
  • Wall 2 & 4 Area (Breadth × Height): 6 m × 15 m = 90 m²
  • Similarly, the combined area of these two walls is 90 m² × 2 = 180 m².

So, the total surface area of the four walls is 300 m² + 180 m² = 480 m².

2. Ceiling

The ceiling is a rectangle with dimensions equal to the length and breadth of the room. Therefore, its area is:

  • Ceiling Area (Length × Breadth): 10 m × 6 m = 60 m²

3. Total Surface Area to be Painted

Now, we add the total wall area to the ceiling area to find the total surface area that needs to be painted:

  • Total Area: 480 m² (walls) + 60 m² (ceiling) = 540 m²

So, guys, we've figured out that we need to paint a whopping 540 square meters! That’s a lot of wall space. This calculation is crucial because it directly impacts how much paint you'll need and, of course, the total cost.

Calculating the Cost of Painting

Now that we know the surface area, let's calculate the cost. The problem states that the painting cost is ₹5 per square meter. This is a straightforward multiplication problem:

  • Cost per Square Meter: ₹5
  • Total Area: 540 m²

To find the total cost, we multiply these two values:

  • Total Cost: ₹5/m² × 540 m² = ₹2700

Therefore, the total cost of painting the walls and ceiling of the room is ₹2700. See? Math isn't just about numbers; it's about solving real-life problems like this one!

Key Concepts Revisited

Let’s quickly recap the key concepts we used to solve this problem. This will help solidify your understanding and make similar problems a breeze.

  • Surface Area of a Rectangle: The area of a rectangle is calculated by multiplying its length and breadth (Area = Length × Breadth).
  • Total Surface Area: To find the total surface area of the walls, we calculated the area of each wall and then added them together. We also calculated the ceiling area separately.
  • Cost Calculation: We found the total painting cost by multiplying the total surface area by the cost per square meter.

Understanding these concepts is super useful, not just for math problems but for everyday tasks like home improvement projects or even estimating material costs for various jobs.

Real-World Applications

This problem isn't just an academic exercise; it has real-world applications. Think about it:

  • Home Improvement: When planning to paint a room, you need to know how much paint to buy. This calculation helps you estimate the surface area accurately, preventing you from buying too much or too little paint.
  • Construction and Renovation: Contractors use these calculations to estimate costs for painting, wallpapering, or other surface treatments.
  • Interior Design: Designers use surface area calculations to plan layouts, choose materials, and estimate costs for various projects.
  • DIY Projects: If you’re a DIY enthusiast, understanding these concepts can save you time and money on various projects around the house.

So, whether you're a student, a homeowner, or a professional, these basic mathematical concepts are incredibly valuable. Knowing how to calculate surface area and costs can help you make informed decisions and manage your resources effectively.

Tips for Solving Similar Problems

Want to ace similar problems in the future? Here are a few tips to keep in mind:

  • Draw a Diagram: Visualizing the problem often helps. Sketch a simple diagram of the room and label the dimensions. This makes it easier to see which surfaces need to be calculated.
  • Break it Down: Divide the problem into smaller, manageable steps. Calculate the area of each wall separately, then the ceiling, and finally add them up. This reduces the chance of errors.
  • Double-Check Units: Make sure all dimensions are in the same units (meters in this case). If not, convert them before you start calculating.
  • Use Formulas: Remember the basic formulas for area calculations. Knowing the formula for the area of a rectangle (Length × Breadth) is crucial.
  • Practice: The more you practice, the better you'll get. Try solving similar problems with different dimensions to build your confidence.

Conclusion

So, guys, we've successfully solved a real-world problem by calculating the surface area of a room and the cost of painting it. We learned how to break down the problem, apply basic formulas, and arrive at a practical solution. Remember, math isn't just about numbers; it’s a tool that helps us understand and navigate the world around us.

By understanding the concepts of surface area and cost calculation, you can tackle similar problems with confidence. Whether it’s planning a home makeover or estimating costs for a project, these skills will come in handy. Keep practicing, stay curious, and remember that every problem is just a puzzle waiting to be solved!