Math Problem Statement

How long would it take to paint the inside of this room?

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:

  1. 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 = 8.5×2.8=23.8m28.5 \times 2.8 = 23.8 \, \text{m}^2 per wall.
      • Two such walls: 23.8×2=47.6m223.8 \times 2 = 47.6 \, \text{m}^2.
      • Side walls (6.0m × 2.8m) each = 6.0×2.8=16.8m26.0 \times 2.8 = 16.8 \, \text{m}^2 per wall.
      • Two such walls: 16.8×2=33.6m216.8 \times 2 = 33.6 \, \text{m}^2.
      • Total wall area = 47.6+33.6=81.2m247.6 + 33.6 = 81.2 \, \text{m}^2.
  2. Subtract the area of the door:

    • Door area = 2.1×1.0=2.1m22.1 \times 1.0 = 2.1 \, \text{m}^2.
    • Wall area to paint = 81.22.1=79.1m281.2 - 2.1 = 79.1 \, \text{m}^2.
  3. Painting time:

    • Time to paint 1 coat of 1m² = 10 minutes.
    • Time to paint 1 coat of the entire room = 79.1×10=791minutes79.1 \times 10 = 791 \, \text{minutes}.
    • Since two coats are needed: 791×2=1582minutes791 \times 2 = 1582 \, \text{minutes}.
  4. Convert to hours:

    • Total time in hours = 15826026.37hours\frac{1582}{60} \approx 26.37 \, \text{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:

  1. What would be the time if the painter took 8 minutes per square meter instead?
  2. How would the result change if the door's size was doubled?
  3. If the painter could paint 2m² every 10 minutes, what would be the new time?
  4. How much time would it take to paint only one coat?
  5. 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