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 thembekamvelase78, good to see you again. Here are the solutions for question 4.1: 4.1.1 Step 1: Identify the diameter of one cork from the diagram. The diagram shows the diameter of a cylindrical cork is 20 mm. Step 2: Calculate the radius. The radius is half of the diameter. Radius = Diameter2 = 20 mm2 = 10 mm The radius of one cork is 10 mm. 4.1.2 Step 1: Identify the inner height and border width from the diagram. The inner height of the pin board is 309 mm. The border width is 4 cm on the top and 4 cm on the bottom. Step 2: Convert the border width from cm to mm. 4 cm = 4 × 10 mm = 40 mm Step 3: Calculate the total outside height. The outside height includes the inner height plus the top and bottom borders. Outside height = 309 mm + 40 mm + 40 mm = 389 mm Step 4: Round the outside height to the nearest 100 mm. 389 mm is closer to 400 mm than to 300 mm. The outside height of the pin board with the border, rounded to the nearest 100 mm, is 400 mm. 4.1.3 Step 1: Calculate the surface area of one cork. The radius r = 10 mm = 0.01 m. The height h = 43 mm = 0.043 m. Using the formula: Total surface area of a cylinder = 2 × 3.142 × radius^2 + 2 × 3.142 × radius × height SA_cork = (2 × 3.142 × (0.01 m)^2) + (2 × 3.142 × 0.01 m × 0.043 m) SA_cork = (2 × 3.142 × 0.0001 m^2) + (2 × 3.142 × 0.00043 m^2) SA_cork = 0.0006284 m^2 + 0.00270196 m^2 SA_cork = 0.00333036 m^2 Step 2: Calculate the total surface area to be painted for all corks and layers. Lareb collected 53 corks and painted each with 3 layers. Total SA_painted = SA_cork × 53 corks × 3 layers Total SA_painted = 0.00333036 m^2 × 53 × 3 Total SA_painted = 0.00333036 m^2 × 159 = 0.52922724 m^2 Step 3: Calculate the total volume of paint needed. The spread rate is 3 m^2 per litre. Volume of paint = Total SA_paintedSpread rate = 0.52922724 m^23 m^2/L Volume of paint = 0.17640908 L Step 4: Calculate the number of paint cans required. The paint is sold in 125 ml cans. Convert the volume of paint to ml. 0.17640908 L = 0.17640908 × 1000 ml = 176.40908 ml Number of cans needed: Number of cans = 176.40908 ml125 ml/can = 1.41127264 cans Since you cannot buy a fraction of a can, Lareb must buy 2 cans. Step 5: Calculate the total cost of the paint. Each can costs R55.00. Total cost = 2 cans × R55.00/can = R110.00 The total cost of the paint required is R110.00. Send me the next one 📸