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
2.1.1 Step 1: Identify the lengths of all sides of the patio from the diagram. The lengths are 5.5\, m, 3\, m, 2.5\, m, and 3.9\, m. Step 2: Add the lengths of all sides to find the total length of fencing (perimeter). Total length = 5.5\, m + 3\, m + 2.5\, m + 3.9\, m Step 3: Calculate the sum. Total length = 14.9\, m The total length of the fencing required is 14.9 m. 2.1.2 Step 1: Calculate the radius (r) of the fire pit from its diameter. Given diameter (D) = 91.44\, cm. r = (D)/(2) = 91.44\, cm2 = 45.72\, cm Step 2: Substitute the radius and given height (h = 30.48\, cm) into the lateral surface area formula. Lateral surface area = 2 × 3.142 × r × h Lateral surface area = 2 × 3.142 × 45.72\, cm × 30.48\, cm Step 3: Calculate the lateral surface area. Lateral surface area = 8760.96672\, cm^2 Rounding to two decimal places: Lateral surface area ≈ 8760.97\, cm^2 The lateral surface area of the fire pit is 8760.97 cm^2. 2.2.1 The map scale represents the ratio of a distance on the map to the corresponding actual distance in reality. 2.2.2 Step 1: Divide the first part of the ratio (25) by 25 to get 1. (25)/(25) = 1 Step 2: Divide the second part of the ratio (10 000 000) by 25. (10\,000\,000)/(25) = 400\,000 The map scale as a unit ratio is 1 : 400 000. 2.2.3 Step 1: Calculate the actual distance in cm using the unit ratio from 2.2.2 (1 cm on map = 400 000 cm in reality). Given map distance = 10.8\, cm. Actual distance in cm = 10.8\, cm × 400\,000 Actual distance in cm = 4\,320\,000\, cm Step 2: Convert the actual distance from cm to km. (Note: 1\, km = 100\,000\, cm). Actual distance in km = 4\,320\,000\, cm100\,000\, cm/km Step 3: Calculate the actual distance in km. Actual distance in km = 43.2\, km The actual distance between the two towns is 43.2 km. 2.2.4 Step 1: Convert Phumeza's estimated distance from cm to km. Estimated distance = 5\,400\,000\, cm. Estimated distance in km = 5\,400\,000\, cm100\,000\, cm/km = 54\, km Step 2: Calculate the travel time using the formula Time = Distance/Speed. Given speed = 120\, km/h. Time = 54\, km120\, km/h = 0.45\, hours Step 3: Convert the travel time from hours to minutes. Travel time in minutes = 0.45\, hours × 60\, minutes/hour = 27\, minutes Step 4: Calculate the arrival time by adding the travel time to the departure time (08:00 a.m.). Arrival time = 08:00\, a.m. + 27\, minutes = 08:27\, a.m. Step 5: Compare the arrival time with the desired arrival time (before 09:00 a.m.). Since 08:27 a.m. is before 09:00 a.m., Phumeza's mother will have the possibility of arriving before 09:00 a.m. Phumeza's mother will arrive at 08:27 a.m., which is before 09:00 a.m. That's 2 down. 3 left today — send the next one.