Understand the geometry of Helena's pool.

You're on a roll — here are the solutions for the pool questions: 10.1 Helena calculates that her pool can hold over 30 000 litres of water. If the volume of water for part/section A of her pool is 20 160 l, determine whether Helena is correct. Step 1: Understand the geometry of Helena's pool. Helena's pool is rectangular with a length of 7 m and a width of 4.8 m. The depth increases uniformly from 0.6 m (Depth 1) to 1.2 m (Depth 2). The volume of a pool with uniformly increasing depth can be calculated using the average depth. Step 2: Calculate the average depth of Helena's pool. Average Depth = Depth 1 + Depth 22 Average Depth = 0.6 m + 1.2 m2 Average Depth = 1.8 m2 Average Depth = 0.9 m Step 3: Calculate the total volume of Helena's pool. Volume_Helena = Length × Width × Average Depth Volume_Helena = 7 m × 4.8 m × 0.9 m Volume_Helena = 30.24 m^3 Step 4: Convert the volume from cubic meters to litres. Given 1 m^3 = 1000 litres. Volume_Helena = 30.24 × 1000 litres Volume_Helena = 30240 litres Step 5: Determine if Helena is correct. Helena calculates her pool can hold over 30 000 litres. Since 30240 litres > 30000 litres, Helena is correct. (Note: The information about "part/section A" having 20 160 l confirms that 7 m × 4.8 m × 0.6 m = 20.16 m^3 = 20160 l, which is consistent with the minimum depth portion of the pool.) Helena is correct. 10.2 If Jay-Jay's pool also holds 30 000 litres of water, then calculate, rounded to one decimal place, the depth of his pool. Step 1: Identify the given information for Jay-Jay's pool. Jay-Jay's pool is cylindrical. Diameter (D) = 4.8 m Volume (V_Jay-Jay) = 30000 litres We need to find the depth (h). Use = 3.14. Step 2: Convert the volume from litres to cubic meters. Given 1 m^3 = 1000 litres. V_Jay-Jay = 30000 litres1000 litres/m^3 V_Jay-Jay = 30 m^3 Step 3: Calculate the radius (r) of Jay-Jay's pool. r = (D)/(2) = 4.8 m2 r = 2.4 m Step 4: Use the formula for the volume of a cylindrical tank to find the depth (h). V = r^2 h 30 m^3 = 3.14 × (2.4 m)^2 × h 30 m^3 = 3.14 × 5.76 m^2 × h 30 m^3 = 18.0864 m^2 × h Step 5: Solve for h and round to one decimal place. h = 30 m^318.0864 m^2 h ≈ 1.6587 m Rounding to one decimal place: h ≈ 1.7 m The depth of Jay-Jay's pool is 1.7 m. 10.3 Jay-Jay and Helena both need to replace the tubing that runs around the top edge of their pools. They know they can get a better deal if they buy in bulk so they combine the length of tubing they each need and then add an extra 10% to be safe. Show, by means of calculations, that together they will need more than 40 m of tubing. Step 1: Calculate the perimeter of Helena's rectangular pool. Perimeter_Helena = 2 × (Length + Width) Perimeter_Helena = 2 × (7 m + 4.8 m) Perimeter_Helena = 2 × (11.8 m) Perimeter_Helena = 23.6 m Step 2: Calculate the circumference (perimeter) of Jay-Jay's cylindrical pool. Circumference_Jay-Jay = × Diameter Circumference_Jay-Jay = 3.14 × 4.8 m Circumference_Jay-Jay = 15.072 m Step 3: Calculate the total length of tubing needed before adding the extra 10%. Total Tubing (initial) = Perimeter_Helena + Circumference_Jay-Jay Total Tubing (initial) = 23.6 m + 15.072 m Total Tubing (initial) = 38.672 m Step 4: Add an extra 10% for safety. Extra 10% = 0.10 × 38.672 m Extra 10% = 3.8672 m