This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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2.2.1 Step 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 cm W = 190 mm10 mm/cm = 19 cm H = 190 mm10 mm/cm = 19 cm Step 2: Calculate the surface area (SA) using the given formula. SA = 2(L × W) + 2(L × H) + 2(W × H) SA = 2(39 cm × 19 cm) + 2(39 cm × 19 cm) + 2(19 cm × 19 cm) SA = 2(741 cm^2) + 2(741 cm^2) + 2(361 cm^2) SA = 1482 cm^2 + 1482 cm^2 + 722 cm^2 SA = 3686 cm^2 The surface area of the concrete block is 3686 cm^2. 2.2.2 Step 1: Use the dimensions in centimeters from 2.2.1. L = 39 cm, W = 19 cm, H = 19 cm. Step 2: Calculate the volume (V) using the given formula. V = L × W × H V = 39 cm × 19 cm × 19 cm V = 14091 cm^3 The volume of the concrete block is 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 Step 1: 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 provinces that can be seen on the map. 3.1.2 Step 1: 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. 3.1.3 Step 1: 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 km^2 Step 2: Convert the percentage to a decimal and solve for A. 0.106 × A = 129437 A = (129437)/(0.106) A ≈ 1221103.77 km^2 The area of the whole of South Africa is approximately 1221103.77 km^2. Last free one today — make it count tomorrow, or type /upgrade for unlimited.