Math Problem Statement

If one can of paint covers 200 square feet, how many cans will I need for my living room that's 20'x16' and has 12' ceilings?

Solution

To determine how many cans of paint you'll need for your living room, we'll follow these steps:

Step 1: Calculate the total square footage of the walls

You have a room with a length of 20 feet, a width of 16 feet, and a height of 12 feet. The room has four walls: two of them are 20 feet long, and the other two are 16 feet long.

To find the surface area of each set of walls:

  • Two 20-foot walls: 2×(20ft×12ft)=2×240=480sq ft2 \times (20 \, \text{ft} \times 12 \, \text{ft}) = 2 \times 240 = 480 \, \text{sq ft}
  • Two 16-foot walls: 2×(16ft×12ft)=2×192=384sq ft2 \times (16 \, \text{ft} \times 12 \, \text{ft}) = 2 \times 192 = 384 \, \text{sq ft}

Now, add the areas together to get the total square footage:

480sq ft+384sq ft=864sq ft480 \, \text{sq ft} + 384 \, \text{sq ft} = 864 \, \text{sq ft}

Step 2: Account for the coverage per can of paint

You mentioned that one can of paint covers 200 square feet. To find the number of cans needed:

864sq ft200sq ft per can=4.32cans\frac{864 \, \text{sq ft}}{200 \, \text{sq ft per can}} = 4.32 \, \text{cans}

Since you can't purchase a fraction of a can, you'll need to round up to the next whole number, meaning 5 cans.

Final Answer:

You will need 5 cans of paint to cover the walls of your living room.

Would you like more details or have any questions about the calculation? Here are some related questions:

  1. How do I calculate the square footage of a room with a slanted ceiling?
  2. What factors should I consider when buying paint aside from coverage?
  3. How much paint should I buy if I plan to paint both walls and a ceiling?
  4. How do I calculate how much paint I need for a textured wall?
  5. How can I estimate the amount of paint needed for trim or doors?

Tip: When painting, consider the type of wall (smooth, textured, etc.) as it can affect the amount of paint needed. Textured surfaces require more paint than smooth surfaces.

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Math Problem Analysis

Mathematical Concepts

Geometry
Surface Area
Division

Formulas

Area of rectangle: length × height
Total number of cans: Total area ÷ Coverage per can

Theorems

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Suitable Grade Level

Grades 6-8