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Calculate the surface area and volume of a concrete block with dimensions 390 mm x 190 mm x 190 mm.

Mathematics

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2.2.1

  1. Convert the dimensions of the concrete block from millimeters to centimeters.

    Given dimensions: Length (L) = 390 mm, Width (W) = 190 mm, Height (H) = 190 mm.
    Since 1 cm = 10 mm:

    L=390 mm10 mm/cm=39 cmL = \frac{390 \text{ mm}}{10 \text{ mm/cm}} = 39 \text{ cm} W=190 mm10 mm/cm=19 cmW = \frac{190 \text{ mm}}{10 \text{ mm/cm}} = 19 \text{ cm} H=190 mm10 mm/cm=19 cmH = \frac{190 \text{ mm}}{10 \text{ mm/cm}} = 19 \text{ cm}
  2. Calculate the surface area (SA) using the given formula.

    SA=2(L×W)+2(L×H)+2(W×H)\text{SA} = 2(\text{L} \times \text{W}) + 2(\text{L} \times \text{H}) + 2(\text{W} \times \text{H}) SA=2(39 cm×19 cm)+2(39 cm×19 cm)+2(19 cm×19 cm)\text{SA} = 2(39 \text{ cm} \times 19 \text{ cm}) + 2(39 \text{ cm} \times 19 \text{ cm}) + 2(19 \text{ cm} \times 19 \text{ cm}) SA=2(741 cm2)+2(741 cm2)+2(361 cm2)\text{SA} = 2(741 \text{ cm}^2) + 2(741 \text{ cm}^2) + 2(361 \text{ cm}^2) SA=1482 cm2+1482 cm2+722 cm2\text{SA} = 1482 \text{ cm}^2 + 1482 \text{ cm}^2 + 722 \text{ cm}^2 SA=3686 cm2\text{SA} = 3686 \text{ cm}^2

    The surface area of the concrete block is 3686 cm2\boxed{\text{3686 cm}^2}.

    2.2.2

  3. Use the dimensions in centimeters from 2.2.1.

    L = 39 cm, W = 19 cm, H = 19 cm.

  4. Calculate the volume (V) using the given formula.

    V=L×W×H\text{V} = \text{L} \times \text{W} \times \text{H} V=39 cm×19 cm×19 cm\text{V} = 39 \text{ cm} \times 19 \text{ cm} \times 19 \text{ cm} V=14091 cm3\text{V} = 14091 \text{ cm}^3

    The volume of the concrete block is 14091 cm3\boxed{\text{14091 cm}^3}.

    2.2.3
    The "RDP plans in 2.1" or the "floor plan" which contain the dimensions of the external walls of the RDP house are not provided in the image. Without these dimensions, it is not possible to calculate the total area of the walls and subsequently the number of pallets of concrete blocks required.

    2.2.4
    The number of concrete blocks calculated in 2.2.3 is an estimation because it does not account for factors such as breakages during transport or construction, wastage from cutting blocks to fit specific areas (e.g., around windows or doors), or the mortar joints between blocks which reduce the number of blocks needed for a given area.

    3.1.1

  5. Identify the provinces bordering the Free State on the map.

    The provinces visible on the map are:

    • North West
    • Gauteng
    • Mpumalanga
    • Kwazulu Natal
    • Eastern Cape
    • Northern Cape There are 6\boxed{\text{6}} provinces that can be seen on the map.

    3.1.2

  6. Locate Bloemfontein and the N1 route towards the Northern Cape on the map.

    Following the N1 south from Bloemfontein towards the Northern Cape, the next town indicated on the route is Trompsburg.
    The town you will find next to the N1 on route from Bloemfontein to the Northern Cape is Trompsburg\boxed{\text{Trompsburg}}.

    3.1.3

  7. Set up the equation based on the given information.

    The area of the Free State is 129 437 km², which forms 10.6% of the area of the whole of South Africa.
    Let A be the total area of South Africa.

    10.6%×A=129437 km210.6\% \times \text{A} = 129437 \text{ km}^2
  8. Convert the percentage to a decimal and solve for A.

    0.106×A=1294370.106 \times \text{A} = 129437 A=1294370.106\text{A} = \frac{129437}{0.106} A≈1221103.77 km2\text{A} \approx 1221103.77 \text{ km}^2

    The area of the whole of South Africa is approximately 1221103.77 km2\boxed{\text{1221103.77 km}^2}.

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