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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 di... 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 surface area of the two walls, we first calculate the area of each wall.

  • The length of one wall is 4.8 m and the height is 2.75 m:

    extAreaofWall1=4.8imes2.75=13.2extm2 ext{Area of Wall 1} = 4.8 imes 2.75 = 13.2 ext{ m}^2

  • The length of the second wall is 3.5 m and the same height of 2.75 m:

    extAreaofWall2=3.5imes2.75=9.625extm2 ext{Area of Wall 2} = 3.5 imes 2.75 = 9.625 ext{ m}^2

  • Adding these two areas gives:

    extTotalSurfaceArea=13.2+9.625=22.825extm2 ext{Total Surface Area} = 13.2 + 9.625 = 22.825 ext{ m}^2

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 use the total surface area and the thickness of the plaster.

  • The thickness of the plaster is 12 mm, which is equivalent to 1.2 cm. Thus, we can find the volume:

    extVolumeofPlaster=extAreaofWallsimesextThickness=22.825extm2imes1.2extcm ext{Volume of Plaster} = ext{Area of Walls} imes ext{Thickness} = 22.825 ext{ m}^2 imes 1.2 ext{ cm}

    Recall that 1 m² = 10,000 cm², so:

    =(22.825imes10,000)imes1.2=273,900extcm3= (22.825 imes 10,000) imes 1.2 = 273,900 ext{ cm}^3

Step 3

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

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Answer

To determine the number of bags needed:

  • The volume of plaster required is 273,900 cm³. Since one bag covers 15,000 cm³, we find the number of bags needed:

    extNumberofBags=273,900extcm315,000extcm3=18.26 ext{Number of Bags} = \frac{273,900 ext{ cm}^3}{15,000 ext{ cm}^3} = 18.26

Since Unathi cannot buy a fraction of a bag, he will need to round up to 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, we need to calculate the perimeter of the room.

  • The perimeter can be calculated using the formula:

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

    Plugging in the values:

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

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

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