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
Here's the solution to the problems: 4.3.1) Step 1: Use the given conversion factor. Given that 1\, = 1000\, cm^3. Step 2: Convert the volume from litres to cubic centimetres. 215\, × 1000\, cm^31\, = 215000\, cm^3 The volume is 215000 cm^3. 215000\, cm^3 4.3.2) Step 1: State the formula for the volume of a cylinder and the given values. The formula for the volume of a cylinder is V = r^2 h. From 4.3.1, V = 215000\, cm^3. The radius is r = 26\, cm. Use = 3.14. Step 2: Substitute the values into the volume formula. 215000\, cm^3 = (3.14) × (26\, cm)^2 × h Step 3: Calculate r^2. 215000\, cm^3 = (3.14) × (676\, cm^2) × h Step 4: Multiply by r^2. 215000\, cm^3 = 2122.64\, cm^2 × h Step 5: Solve for h. h = 215000\, cm^32122.64\, cm^2 h ≈ 101.288\, cm Step 6: Round the height to the nearest whole number as requested (approximately 101 cm). h ≈ 101\, cm The height of the drum is approximately 101 cm. 101\, cm 4.3.3) Step 1: State the formula for the surface area of a cylinder and the given values. The formula for the surface area is A = 2 r^2 + 2 rh. The radius is r = 26\, cm. The height is h = 101\, cm (from 4.3.2). Use = 3.14. Step 2: Substitute the values into the surface area formula. A = 2 × (3.14) × (26\, cm)^2 + 2 × (3.14) × (26\, cm) × (101\, cm) Step 3: Calculate the terms. A = 2 × 3.14 × 676\, cm^2 + 2 × 3.14 × 26\, cm × 101\, cm A = 4245.28\, cm^2 + 16479.28\, cm^2 Step 4: Add the terms to find the total surface area. A = 20724.56\, cm^2 The surface area of the oil drum is 20724.56 cm^2. 20724.56\, cm^2 4.3.4) Step 1: State the relationship between diameter and radius. The diameter D is twice the radius r. D = 2r Step 2: Substitute the given radius. The radius is r = 26\, cm. D = 2 × 26\, cm D = 52\, cm The diameter of the tank is 52 cm. 52\, cm That's 2 down. 3 left today — send the next one.