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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 were not plastered. The dimensions of the floor of this bedroom are 4,8 m × 3,5 m, as shown in the dia... show full transcript

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

Step 1

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

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Answer

To find the total surface area of the two walls that need plastering, we need to calculate the area for both walls separately and then sum them up.

  1. Calculate the area of the first wall:

    The dimensions are:

    • Height = 2.75 m
    • Length = 4.8 m

    Using the formula for area:

    A1=extheightimesextlength=2.75imes4.8=13.2extm2A_1 = ext{height} imes ext{length} = 2.75 imes 4.8 = 13.2 ext{ m}^2

  2. Calculate the area of the second wall:

    The dimensions are:

    • Height = 2.75 m
    • Length = 3.5 m

    Again, using the area formula:

    A2=extheightimesextwidth=2.75imes3.5=9.625extm2A_2 = ext{height} imes ext{width} = 2.75 imes 3.5 = 9.625 ext{ m}^2

  3. Total surface area for two walls:

    By adding both areas:

    Aexttotal=A1+A2=13.2+9.625=22.825extm2A_{ ext{total}} = A_1 + A_2 = 13.2 + 9.625 = 22.825 ext{ m}^2

Thus, the total surface area of the two walls is 22.825 m².

Step 2

3.1.2 Determine, in cm³, the volume of plaster required to plaster these two walls.

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Answer

To calculate the volume of plaster required, we will use the total surface area from the previous step.

  1. Convert area from m² to cm²:

    Since 1 m² = 10,000 cm²:

    Aexttotalincm2=22.825extm2imes10,000=228,250extcm2A_{ ext{total in cm}^2} = 22.825 ext{ m}^2 imes 10,000 = 228,250 ext{ cm}^2

  2. Calculate volume of plaster:

    The thickness of the plaster is 12 mm, which is equal to 1.2 cm.

    We apply the formula for volume:

    V=Aimesextthickness=228,250extcm2imes1.2extcm=273,900extcm3V = A imes ext{thickness} = 228,250 ext{ cm}^2 imes 1.2 ext{ cm} = 273,900 ext{ cm}^3

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

Step 3

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

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Answer

To find the number of bags required for the plaster:

  1. Determine the volume each bag covers:

    Each bag covers 15,000 cm³ of plaster.

  2. Calculate the number of bags needed:

    Using the formula:

    ext{Number of bags} = rac{ ext{Total Volume}}{ ext{Volume per bag}} = rac{273,900 ext{ cm}^3}{15,000 ext{ cm}^3} = 18.26

  3. Round up to the nearest whole number:

    Since you cannot purchase a fraction of a bag, round up:

    Minimum number of bags needed = 19 bags.

Step 4

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

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Answer

To find the total length of the new cornices:

  1. Calculate the perimeter of the room:

    Using the perimeter formula:

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

    Plugging in the values:

    P=2imes(4.8extm+3.5extm)=2imes8.3=16.6extmP = 2 imes (4.8 ext{ m} + 3.5 ext{ m}) = 2 imes 8.3 = 16.6 ext{ m}

Thus, the total length of the new cornices is 16.6 metres.

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