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 $7 \text{ m}$ and a width of $4.8 \text{ m}$. The depth increases uniformly from $0.6 \text{ m}$ (Depth 1) to $1.2 \text{ m}$ (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. $$\text{Average Depth} = \frac{\text{Depth 1} + \text{Depth 2}}{2}$$ $$\text{Average Depth} = \frac{0.6 \text{ m} + 1.2 \text{ m}}{2}$$ $$\text{Average Depth} = \frac{1.8 \text{ m}}{2}$$ $$\text{Average Depth} = 0.9 \text{ m}$$ Step 3: Calculate the total volume of Helena's pool. $$\text{Volume}_{\text{Helena}} = \text{Length} \times \text{Width} \times \text{Average Depth}$$ $$\text{Volume}_{\text{Helena}} = 7 \text{ m} \times 4.8 \text{ m} \times 0.9 \text{ m}$$ $$\text{Volume}_{\text{Helena}} = 30.24 \text{ m}^3$$ Step 4: Convert the volume from cubic meters to litres. Given $1 \text{ m}^3 = 1000 \text{ litres}$. $$\text{Volume}_{\text{Helena}} = 30.24 \times 1000 \text{ litres}$$ $$\text{Volume}_{\text{Helena}} = 30240 \text{ litres}$$ Step 5: Determine if Helena is correct. Helena calculates her pool can hold over 30 000 litres. Since $30240 \text{ litres} > 30000 \text{ litres}$, Helena is correct. (Note: The information about "part/section A" having 20 160 l confirms that $7 \text{ m} \times 4.8 \text{ m} \times 0.6 \text{ m} = 20.16 \text{ m}^3 = 20160 \text{ l}$, which is consistent with the minimum depth portion of the pool.) Helena is $\boxed{\text{correct}}$. 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 ($D$) = $4.8 \text{ m}$ Volume ($V_{\text{Jay-Jay}}$) = $30000 \text{ litres}$ We need to find the depth ($h$). Use $\pi = 3.14$. Step 2: Convert the volume from litres to cubic meters. Given $1 \text{ m}^3 = 1000 \text{ litres}$. $$V_{\text{Jay-Jay}} = \frac{30000 \text{ litres}}{1000 \text{ litres/m}^3}$$ $$V_{\text{Jay-Jay}} = 30 \text{ m}^3$$ Step 3: Calculate the radius ($r$) of Jay-Jay's pool. $$r = \frac{D}{2} = \frac{4.8 \text{ m}}{2}$$ $$r = 2.4 \text{ m}$$ Step 4: Use the formula for the volume of a cylindrical tank to find the depth ($h$). $$V = \pi r^2 h$$ $$30 \text{ m}^3 = 3.14 \times (2.4 \text{ m})^2 \times h$$ $$30 \text{ m}^3 = 3.14 \times 5.76 \text{ m}^2 \times h$$ $$30 \text{ m}^3 = 18.0864 \text{ m}^2 \times h$$ Step 5: Solve for $h$ and round to one decimal place. $$h = \frac{30 \text{ m}^3}{18.0864 \text{ m}^2}$$ $$h \approx 1.6587 \text{ m}$$ Rounding to one decimal place: $$h \approx 1.7 \text{ m}$$ The depth of Jay-Jay's pool is $\boxed{\text{1.7 m}}$. 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. $$\text{Perimeter}_{\text{Helena}} = 2 \times (\text{Length} + \text{Width})$$ $$\text{Perimeter}_{\text{Helena}} = 2 \times (7 \text{ m} + 4.8 \text{ m})$$ $$\text{Perimeter}_{\text{Helena}} = 2 \times (11.8 \text{ m})$$ $$\text{Perimeter}_{\text{Helena}} = 23.6 \text{ m}$$ Step 2: Calculate the circumference (perimeter) of Jay-Jay's cylindrical pool. $$\text{Circumference}_{\text{Jay-Jay}} = \pi \times \text{Diameter}$$ $$\text{Circumference}_{\text{Jay-Jay}} = 3.14 \times 4.8 \text{ m}$$ $$\text{Circumference}_{\text{Jay-Jay}} = 15.072 \text{ m}$$ Step 3: Calculate the total length of tubing needed before adding the extra 10%. $$\text{Total Tubing (initial)} = \text{Perimeter}_{\text{Helena}} + \text{Circumference}_{\text{Jay-Jay}}$$ $$\text{Total Tubing (initial)} = 23.6 \text{ m} + 15.072 \text{ m}$$ $$\text{Total Tubing (initial)} = 38.672 \text{ m}$$ Step 4: Add an extra 10% for safety. $$\text{Extra 10%} = 0.10 \times 38.672 \text{ m}$$ $$\text{Extra 10%} = 3.8672 \text{ m}$$ $$\text