To determine the volume of water discharged from the hose into the container, we can use the relationship between flow rate, cross-sectional area, and velocity. Let's break down the problem step-by-step. ### Step 1: Understand the Flow Rate The flow rate (Q) of a fluid can be calculated using the formula: \[ Q = A \times v \] where: - \( Q \) is the flow rate in cubic meters per second (m³/s), - \( A \) is the cross-sectional area of the hose in square meters (m²), - \( v \) is the velocity of the fluid in meters per second (m/s). ### Step 2: Plug in the Values From the problem, we know: - The cross-sectional area \( A = 0.5 \, \text{m}^2 \) - The velocity \( v = 60 \, \text{m/s} \) Now, we can calculate the flow rate: \[ Q = 0.5 \, \text{m}^2 \times 60 \, \text{m/s} = 30 \, \text{m}^3/\text{s} \] ### Step 3: Calculate the Total Volume Discharged Next, we need to find out how much water is discharged in 20 seconds. The total volume \( V \) can be calculated using the formula: \[ V = Q \times t \] where: - \( V \) is the total volume in cubic meters (m³), - \( t \) is the time in seconds (s). Substituting the values we have: \[ V = 30 \, \text{m}^3/\text{s} \times 20 \, \text{s} = 600 \, \text{m}^3 \] ### Conclusion Thus, the volume of the container that is filled completely is **600 m³**. ### Explanation of the Options - **Option A: 240 m³** - This is incorrect because it underestimates the volume based on the flow rate and time calculated. - **Option B: 600 m³** - This is the correct answer as derived from the calculations above. - **Option C: 2400 m³** - This is incorrect; it suggests a much larger volume than what is calculated based on the given flow rate and time. - **Option D: 6000 m³** - This is also incorrect; it is significantly larger than the calculated volume and does not align with the flow rate and time. ### Common Pitfalls 1. **Misunderstanding Units**: Ensure that all units are consistent (e.g., area in m², velocity in m/s). 2. **Forgetting to Multiply by Time**: It’s crucial to multiply the flow rate by the time to find the total volume. 3. **Incorrectly Calculating Flow Rate**: Double-check the multiplication of area and velocity to avoid errors in flow rate. ### Revision Summary - The flow rate is calculated using the formula \( Q = A \times v \). - The total volume discharged is found by multiplying the flow rate by the time: \( V = Q \times t \). - For this problem, the correct volume of the container is **600 m³**. - Always ensure units are consistent and remember to multiply by time to find total volume.