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.
ScanSolve AI Answer
Hey Gomolemo, good to see you again. Here are the solutions to your questions. 1.1 Step 1: Convert the wall thickness from centimeters to meters. 35 cm = 0.35 m Step 2: Calculate the inner diameter of the dam. The outer diameter is 6 m, and the wall thickness is 0.35 m on each side. Inner diameter = Outer diameter - 2 × Wall thickness Inner diameter = 6 m - 2 × 0.35 m Inner diameter = 6 m - 0.70 m Inner diameter = 5.3 m Step 3: Calculate the inner radius of the dam. Inner radius (r) = Inner diameter2 r = 5.3 m2 r = 2.65 m Step 4: Calculate the full volume of the dam's interior (the space for water). The dam is a cylinder with height h = 1.7 m. Volume of cylinder = r^2 h Volume_full = × (2.65 m)^2 × 1.7 m Volume_full = × 7.0225 m^2 × 1.7 m Volume_full ≈ 3.14159 × 7.0225 × 1.7 m^3 Volume_full ≈ 37.500 m^3 Step 5: Calculate the volume of water when the dam is 80% full. Volume_water = 0.80 × Volume_full Volume_water = 0.80 × 37.500 m^3 Volume_water = 30.000 m^3 Step 6: Convert the volume of water to kilolitres. Given that 1 m^3 = 1 kl. Volume_water = 30.000 kl The volume of water in the dam is 30.000 kl. 1.2 Step 1: Convert the area from square millimeters to square centimeters to match the height unit. Given height h = 8 cm. Given area A = 1800 mm^2. Since 1 cm = 10 mm, then 1 cm^2 = (10 mm)^2 = 100 mm^2. A = 1800 mm^2100 mm^2/cm^2 A = 18 cm^2 Step 2: Use the formula for the area of a triangle to find the base length. Area = (1)/(2) × base × height 18 cm^2 = (1)/(2) × base × 8 cm Step 3: Solve for the base length. 18 cm^2 = 4 cm × base base = 18 cm^24 cm base = 4.5 cm The base length of the triangle is 4.5 cm. Send me the next one 📸