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A bedroom is 6 m long, 4 m wide, and 2.8 m high. It has a window 1.2 m wide and 1.5 m high, and a door 0.9 m wide and 2.1 m high. Calculate the area to be painted.

Mathematics

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Answer

2 cans\text{2 cans}

Step-by-step solution

6 steps
  1. Calculate the total area of the four walls.

    The bedroom has a length of 6 m6 \text{ m}, a width of 4 m4 \text{ m}, and a height of 2.8 m2.8 \text{ m}.
    The total area of the four walls is given by the perimeter multiplied by the height.

    Perimeter=2×(length+width)\text{Perimeter} = 2 \times (\text{length} + \text{width}) Perimeter=2×(6 m+4 m)=2×10 m=20 m\text{Perimeter} = 2 \times (6 \text{ m} + 4 \text{ m}) = 2 \times 10 \text{ m} = 20 \text{ m} Area of walls=Perimeter×height\text{Area of walls} = \text{Perimeter} \times \text{height} Area of walls=20 m×2.8 m=56 m2\text{Area of walls} = 20 \text{ m} \times 2.8 \text{ m} = 56 \text{ m}^2
  2. Calculate the area of the window.

    The window has a width of 1.2 m1.2 \text{ m} and a height of 1.5 m1.5 \text{ m}.

    Area of window=width×height\text{Area of window} = \text{width} \times \text{height} Area of window=1.2 m×1.5 m=1.8 m2\text{Area of window} = 1.2 \text{ m} \times 1.5 \text{ m} = 1.8 \text{ m}^2
  3. Calculate the area of the door.

    The door has a width of 0.9 m0.9 \text{ m} and a height of 2.1 m2.1 \text{ m}.

    Area of door=width×height\text{Area of door} = \text{width} \times \text{height} Area of door=0.9 m×2.1 m=1.89 m2\text{Area of door} = 0.9 \text{ m} \times 2.1 \text{ m} = 1.89 \text{ m}^2
  4. Calculate the total area to be painted.

    The area to be painted is the total wall area minus the areas of the window and the door.

    Area to be painted=Area of walls−Area of window−Area of door\text{Area to be painted} = \text{Area of walls} - \text{Area of window} - \text{Area of door} Area to be painted=56 m2−1.8 m2−1.89 m2\text{Area to be painted} = 56 \text{ m}^2 - 1.8 \text{ m}^2 - 1.89 \text{ m}^2 Area to be painted=56 m2−3.69 m2=52.31 m2\text{Area to be painted} = 56 \text{ m}^2 - 3.69 \text{ m}^2 = 52.31 \text{ m}^2
  5. Calculate the total litres of paint needed.

    1 litre of paint covers 9 m29 \text{ m}^2.

    Litres needed=Area to be paintedCoverage per litre\text{Litres needed} = \frac{\text{Area to be painted}}{\text{Coverage per litre}} Litres needed=52.31 m29 m2/litre≈5.8122 litres\text{Litres needed} = \frac{52.31 \text{ m}^2}{9 \text{ m}^2/\text{litre}} \approx 5.8122 \text{ litres}
  6. Calculate the number of 5-litre cans to buy.

    Paint is sold in 5-litre cans only. Since Thabiso cannot buy a fraction of a can, he must round up to ensure he has enough paint.

    Number of cans=Litres neededLitres per can\text{Number of cans} = \frac{\text{Litres needed}}{\text{Litres per can}} Number of cans=5.8122 litres5 litres/can≈1.1624 cans\text{Number of cans} = \frac{5.8122 \text{ litres}}{5 \text{ litres/can}} \approx 1.1624 \text{ cans}

    Rounding up to the nearest whole can:

    Number of cans=⌈1.1624⌉=2 cans\text{Number of cans} = \lceil 1.1624 \rceil = 2 \text{ cans}

    Thabiso needs to buy 2 cans\boxed{\text{2 cans}} of paint.

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