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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Fresh day KIMBE, let's solve. a) Step 1: Identify the dimensions of the rectangular floor. Length (L) = 18 m, Width (W) = 12 m. Step 2: Calculate the area of the rectangular floor. Area = L × W Area = 18 m × 12 m Area = 216 m^2 The area of the rectangular floor is 216 m^2. b) Step 1: Find the semi-perimeter (s) of the triangular cross-section. The sides of the triangle are a = 7 m, b = 7 m, and c = 12 m. s = (a+b+c)/(2) s = 7 m + 7 m + 12 m2 s = 26 m2 s = 13 m Step 2: Use Heron's Formula to find the cross-sectional area of the triangle. Area_triangle = sqrt(s(s-a)(s-b)(s-c)) Area_triangle = sqrt(13(13-7)(13-7)(13-12)) Area_triangle = sqrt(13 × 6 × 6 × 1) Area_triangle = sqrt(13 × 36) Area_triangle = sqrt(468) Area_triangle ≈ 21.6333 m^2 Step 3: Calculate the volume of the triangular prism roof. The length of the prism is 18 m. Volume_prism = cross-sectional area × length Volume_prism = sqrt(468) m^2 × 18 m Volume_prism ≈ 21.6333 m^2 × 18 m Volume_prism ≈ 389.40 m^3 The volume of the triangular prism roof is 389.40 m^3. c) Step 1: Calculate the total area of the two slant faces. Each slant face has an area of 7 m × 18 m = 126 m^2. Total slant area = 2 × 126 m^2 Total slant area = 252 m^2 Step 2: Calculate the total cost of the roofing iron. The cost is K28 per square metre. Total cost = Total slant area × cost per square metre Total cost = 252 m^2 × K28/m^2 Total cost = K7056 The total cost of roofing iron is K7056. d) (i) Step 1: Identify the dimensions of the cylindrical water tank. Radius (r) = 1.2 m, Height (h) = 2.5 m. Step 2: Calculate the total surface area (TSA) of the closed cylinder. TSA = 2 r^2 + 2 rh TSA = 2 (1.2 m)^2 + 2 (1.2 m)(2.5 m) TSA = 2 (1.44 m^2) + 2 (3 m^2) TSA = 2.88 m^2 + 6 m^2 TSA = 8.88 m^2 TSA ≈ 8.88 × 3.14159265... m^2 TSA ≈ 27.897 m^2 Step 3: Round the total surface area to 2 decimal places. TSA = 27.90 m^2 The total surface area of the water tank is 27.90 m^2. (ii) Step 1: Identify the dimensions of the cylindrical water tank. Radius (r) = 1.2 m, Height (h) = 2.5 m. Step 2: Calculate the volume (V) of the water tank. V = r^2 h V = (1.2 m)^2 (2.5 m) V = (1.44 m^2) (2.5 m) V = 3.6 m^3 V ≈ 3.6 × 3.14159265... m^3 V ≈ 11.3097 m^3 Step 3: Round the volume to 2 decimal places. V = 11.31 m^3 The volume of the water tank is 11.31 m^3. (iii) Step 1: Convert the volume from cubic metres to litres. Given that 1 m^3 = 1000 litres. Volume in litres = 3.6 m^3 × 1000 litres/m^3 Volume in litres = 3600 litres Volume in litres ≈ 11309.73 litres Step 2: Calculate the mass of water in the tank. Given that the density of water is 1 kg per litre. Mass = Volume in litres × density Mass = 3600 litres × 1 kg/litre Mass = 3600 kg Mass ≈ 11309.73 kg Step 3: Round the mass to 2 decimal places. Mass = 11309.73 kg The mass of water in the full tank is 11309.73 kg. Send me the next one 📸