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Unathi bought a house - NSC Mathematical Literacy - Question 3 - 2023 - Paper 2

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Unathi bought a house. Two of the walls in one of the bedrooms are not plastered. The dimensions of the floor of this bedroom are 4,8 m × 3,5 m, as shown in the diag... show full transcript

Worked Solution & Example Answer:Unathi bought a house - NSC Mathematical Literacy - Question 3 - 2023 - Paper 2

Step 1

Calculate, in m², the total surface area of the two walls that need to be plastered.

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Answer

To find the surface area of the two walls that need to be plastered, we first calculate the area of one wall:

  1. Area of each Wall:

    Using the formula:

    extAreaofWall=extlengthimesextheight ext{Area of Wall} = ext{length} imes ext{height}

    The dimensions for one wall are:

    • Length = 4.8 m

    • Height = 2.75 m

    extArea=4.8imes2.75=13.2extm2 ext{Area} = 4.8 imes 2.75 = 13.2 ext{ m²}

  2. Area of the Second Wall:

    The other wall has a width of 3.5 m:

    extArea=3.5imes2.75=9.625extm2 ext{Area} = 3.5 imes 2.75 = 9.625 ext{ m²}

  3. Total Surface Area of Both Walls:

    extTotalArea=13.2+9.625=22.825extm2 ext{Total Area} = 13.2 + 9.625 = 22.825 ext{ m²}

    Hence, the total surface area of the two walls that need to be plastered is approximately 22.83 m².

Step 2

The plaster on the walls has a uniform thickness of 12 mm. Determine, in cm³, the volume of plaster required to plaster these two walls.

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Answer

To calculate the volume of plaster needed, we use the formula:

extVolumeofplaster=extareaofwallsimesextthicknessofplaster ext{Volume of plaster} = ext{area of walls} imes ext{thickness of plaster}

  1. Convert Thickness from mm to cm:

    • Thickness = 12 mm = 1.2 cm

  2. Calculate Volume of Plaster:

    Using the total surface area from the previous step:

    extVolume=22.825extm2imes1.2extcm ext{Volume} = 22.825 ext{ m²} imes 1.2 ext{ cm} =273.9extcm3= 273.9 ext{ cm³}

Hence, the volume of plaster required is 273,900 cm³.

Step 3

Determine the minimum number of bags needed to plaster the two walls.

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Answer

To find the minimum number of bags required:

  1. Calculate Number of Bags:

    • Given that one bag covers 15,000 cm³, we can determine the number of bags:
    ext{Number of bags} = rac{ ext{Volume of plaster}}{ ext{Volume covered by one bag}} = rac{273900}{15000} \\ ext{Number of bags} ≈ 18.26

  2. Round Up:

    • As you cannot purchase a partial bag, we round up to 19 bags.

Step 4

Calculate, in metres, the total length of the new cornices.

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Answer

To calculate the total length of the new cornices, we will first calculate the perimeter of the room using the formula:

extPerimeter=2imes(extlength+extwidth) ext{Perimeter} = 2 imes ( ext{length} + ext{width})

  1. Calculate Perimeter:

    • Length = 4.8 m
    • Width = 3.5 m
    extPerimeter=2imes(4.8+3.5) ext{Perimeter} = 2 imes (4.8 + 3.5) =2imes8.3=16.6extm= 2 imes 8.3 = 16.6 ext{ m}

Thus, the total length of the new cornices needed is 16.6 m.

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