Math Problem Statement
Solution
The image asks how long it will take to paint the inside of a room. Below is a breakdown of the problem and its solution:
Details from the image:
- Room dimensions: 8.5m long, 6.0m wide, 2.8m high.
- There is one door that is 2.1m high and 1.0m wide.
- The painter takes 10 minutes to paint 1m², and two coats are required.
- The ceiling is not being painted.
Steps to solve:
-
Surface Area Calculation (excluding the ceiling):
- Total wall area = sum of the areas of all four walls.
- Front and back walls (8.5m × 2.8m) each = per wall.
- Two such walls: .
- Side walls (6.0m × 2.8m) each = per wall.
- Two such walls: .
- Total wall area = .
- Total wall area = sum of the areas of all four walls.
-
Subtract the area of the door:
- Door area = .
- Wall area to paint = .
-
Painting time:
- Time to paint 1 coat of 1m² = 10 minutes.
- Time to paint 1 coat of the entire room = .
- Since two coats are needed: .
-
Convert to hours:
- Total time in hours = .
- Rounding to the nearest whole number = 26 hours.
Final Answer:
It will take 26 hours to paint the inside of the room.
Would you like further details or clarifications?
Here are 5 related questions for further practice:
- What would be the time if the painter took 8 minutes per square meter instead?
- How would the result change if the door's size was doubled?
- If the painter could paint 2m² every 10 minutes, what would be the new time?
- How much time would it take to paint only one coat?
- How would the calculation differ if the ceiling was also being painted?
Tip: When calculating areas for painting, always check if there are objects like windows or doors to exclude from the total surface area.
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Math Problem Analysis
Mathematical Concepts
Geometry
Surface Area Calculation
Unit Conversion
Formulas
Area of a rectangle = length × height
Total painting time = (surface area × painting time per m² × number of coats) / 60
Theorems
Basic Geometry Theorems
Suitable Grade Level
Grades 6-8
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