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Calculate the area of the walls to be painted in Thabiso's bedroom, excluding the door and window.

Mathematics

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5 parts
2.1

4.05 m24.05 \text{ m}^2

2.2

39.11 m239.11 \text{ m}^2

2.3

31.288 litres31.288 \text{ litres}

2.4

7 cans7 \text{ cans}

2.5

R1995.00\text{R}1995.00

Step-by-step solution

10 steps

Here are the calculations for Thabiso's bedroom painting project.

Part 2.1· 3 steps

Calculate the total combined area of the door and the window.

  1. Calculate the area of the door.

    Area of door=height×width=2.1 m×0.9 m=1.89 m2\text{Area of door} = \text{height} \times \text{width} = 2.1 \text{ m} \times 0.9 \text{ m} = 1.89 \text{ m}^2

  2. Calculate the area of the window.

    Area of window=height×width=1.2 m×1.8 m=2.16 m2\text{Area of window} = \text{height} \times \text{width} = 1.2 \text{ m} \times 1.8 \text{ m} = 2.16 \text{ m}^2

  3. Calculate the total combined area of the door and window.

    Total combined area=1.89 m2+2.16 m2=4.05 m2\text{Total combined area} = 1.89 \text{ m}^2 + 2.16 \text{ m}^2 = \boxed{4.05 \text{ m}^2}

Part 2.2

39.11 m239.11 \text{ m}^2

Calculate the area of the walls that need to be painted.

  1. Calculate the total area of the four walls.

    The perimeter of the room is 2×(length+width)2 \times (\text{length} + \text{width}).

    Perimeter=2×(4.5 m+3.8 m)=2×8.3 m=16.6 m\text{Perimeter} = 2 \times (4.5 \text{ m} + 3.8 \text{ m}) = 2 \times 8.3 \text{ m} = 16.6 \text{ m}

    Total area of walls = Perimeter ×\times Height

    Total area of walls=16.6 m×2.6 m=43.16 m2\text{Total area of walls} = 16.6 \text{ m} \times 2.6 \text{ m} = 43.16 \text{ m}^2

  2. Calculate the area to be painted by subtracting the combined area of the door and window from the total wall area.

    Area to be painted=Total area of walls−Area of door and window\text{Area to be painted} = \text{Total area of walls} - \text{Area of door and window} Area to be painted=43.16 m2−4.05 m2=39.11 m2\text{Area to be painted} = 43.16 \text{ m}^2 - 4.05 \text{ m}^2 = \boxed{39.11 \text{ m}^2}

Part 2.3

31.288 litres31.288 \text{ litres}

Thabiso needs double coat of paint for the entire room. Calculate the number of litres of paint required to paint the walls.

  1. Calculate the total area to be covered with a double coat.

    Area for double coat=2×Area to be painted=2×39.11 m2=78.22 m2\text{Area for double coat} = 2 \times \text{Area to be painted} = 2 \times 39.11 \text{ m}^2 = 78.22 \text{ m}^2

  2. Calculate the number of litres of paint required.

    Given that 1 litre of paint covers 2.5 m2^2.

    Litres of paint=Area for double coatCoverage per litre=78.22 m22.5 m2/litre=31.288 litres\text{Litres of paint} = \frac{\text{Area for double coat}}{\text{Coverage per litre}} = \frac{78.22 \text{ m}^2}{2.5 \text{ m}^2/\text{litre}} = \boxed{31.288 \text{ litres}}

Part 2.4

7 cans7 \text{ cans}

Determine the minimum number of 5-litre paint cans Thabiso must buy to paint the walls of the room.

  1. Divide the total litres of paint needed by the volume per can.

    Number of cans=Total litres of paintLitres per can=31.288 litres5 litres/can=6.2576 cans\text{Number of cans} = \frac{\text{Total litres of paint}}{\text{Litres per can}} = \frac{31.288 \text{ litres}}{5 \text{ litres/can}} = 6.2576 \text{ cans}

  2. Round up to the nearest whole number since Thabiso cannot buy a fraction of a can.

    Minimum number of cans=⌈6.2576⌉=7 cans\text{Minimum number of cans} = \lceil 6.2576 \rceil = \boxed{7 \text{ cans}}

Part 2.5

R1995.00\text{R}1995.00

Calculate the total cost of the paint needed to paint the walls of the room.

  1. Multiply the minimum number of cans by the cost per can.

    Total cost=Number of cans×Cost per can=7×R285.00=R1995.00\text{Total cost} = \text{Number of cans} \times \text{Cost per can} = 7 \times \text{R}285.00 = \boxed{\text{R}1995.00}
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