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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Here are the solutions to the questions: 1.9.2 The dimensions of the pool (length and breadth) and the pool cover are not provided in the question. Therefore, it is not possible to determine how many times larger the area of the pool cover is compared to the area of the pool. 1.10.1 The length and breadth of the pool are not provided in the question. Step 1: Calculate the average depth of the pool. Average depth = Shallow end depth + Deep end depth2 = 1 m + 2 m2 = 1.5 m Step 2: Express the total capacity (volume) of the pool using variables for length and breadth. Let L be the length and B be the breadth of the pool. Volume = Length × Breadth × Average depth Volume = L × B × 1.5 m^3 To convert to litres, use 1 m^3 = 1000 litres. Volume = 1.5 × L × B × 1000 litres = 1500LB litres The total capacity of the pool is 1500LB litres, where L and B are the length and breadth of the pool in meters, respectively. 1.10.2 The total volume of the pool (from 1.10.1) is required to answer this question, but the length and breadth of the pool are not provided. Step 1: Determine the amount of chlorine in litres per 1000 litres of pool water. Given: 1.5 teaspoons per 1000 litres of pool water. Given: 1 teaspoon = 5 ml. 1.5 teaspoons = 1.5 × 5 ml = 7.5 ml Convert ml to litres: 7.5 ml = (7.5)/(1000) litres = 0.0075 litres So, 0.0075 litres of chlorine are needed for every 1000 litres of pool water. Step 2: Express the total litres of chlorine required using the pool's volume. Let V_pool be the volume of the pool in litres. Litres of chlorine = V_pool1000 litres × 0.0075 litres Substituting V_pool = 1500LB litres from 1.10.1: Litres of chlorine = (1500LB)/(1000) × 0.0075 = 1.5LB × 0.0075 = 0.01125LB litres The number of litres of chlorine required is 0.01125LB litres, where L and B are the length and breadth of the pool in meters. 1.11.1 Step 1: Identify the given filling rate and conversion factor. Given: Filling rate = 9 gallons per minute. Given: 1 gallon = 3.78541 litres. Step 2: Convert the filling rate from gallons per minute to litres per minute. Litres per minute = 9 gallons/minute × 3.78541 litres/gallon Litres per minute = 34.06869 litres/minute Litres per minute ≈ 34.07 litres/minute 1.11.2 The total volume of the pool (from 1.10.1) is required to answer this question, but the length and breadth of the pool are not provided. Step 1: State the formula for time taken. Time = Total Volume of PoolFilling Rate Step 2: Substitute the expressions for total volume and filling rate. From 1.10.1, V_pool = 1500LB litres. From 1.11.1, Filling Rate = 34.06869 litres/minute. Time in minutes = 1500LB litres34.06869 litres/minute Time in minutes ≈ 44.028LB minutes Step 3: Convert the time from minutes to days. Time in days = Time in minutes60 minutes/hour × 24 hours/day Time in days = (44.028LB)/(1440) days Time in days ≈ 0.030575LB days The time taken to fill the pool is approximately 0.030575LB days, where L and B are the length and breadth of the pool in meters. The final answer would need to be rounded up to the nearest day once numerical values for L and B are known. 1.12 No question was asked for section 1.12. The provided information describes the dimensions of a fire pit. Send me the next one 📸