To determine the pressure at a depth of 10 meters in a fluid at rest, we can use the hydrostatic pressure formula. Let's break down the steps to find the correct answer and understand why it is correct. ### Step-by-Step Explanation 1. **Understanding Hydrostatic Pressure**: The pressure at a certain depth in a fluid is given by the formula: \[ P = \rho g h \] where: - \( P \) is the pressure at depth, - \( \rho \) is the density of the fluid (in kg/m³), - \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)), - \( h \) is the depth in meters. 2. **Identifying the Values**: - The density of water (\( \rho \)) is given as \( 1000 \, \text{kg/m}^3 \). - The depth (\( h \)) is \( 10 \, \text{m} \). - The acceleration due to gravity (\( g \)) is approximately \( 9.81 \, \text{m/s}^2 \). 3. **Substituting the Values into the Formula**: Now, we can substitute the values into the hydrostatic pressure formula: \[ P = 1000 \, \text{kg/m}^3 \times 9.81 \, \text{m/s}^2 \times 10 \, \text{m} \] 4. **Calculating the Pressure**: - First, calculate \( 1000 \times 9.81 \): \[ 1000 \times 9.81 = 9810 \, \text{kg/(m·s}^2\text{)} = 9810 \, \text{Pa} \] - Now, multiply by the depth (10 m): \[ P = 9810 \, \text{Pa} \times 10 = 98100 \, \text{Pa} \] - Since \( 1 \, \text{kPa} = 1000 \, \text{Pa} \), we convert \( 98100 \, \text{Pa} \) to kilopascals: \[ P = \frac{98100 \, \text{Pa}}{1000} = 98.1 \, \text{kPa} \] 5. **Final Answer**: Rounding \( 98.1 \, \text{kPa} \) gives us approximately \( 100 \, \text{kPa} \). Therefore, the correct option is **B. 100 kPa**. ### Explanation of Other Options - **Option A: 50 kPa**: This value is too low. It does not account for the full depth of 10 meters and the density of water. The pressure at this depth is significantly higher than 50 kPa. - **Option C: 200 kPa**: This value is too high. It suggests a depth or density that is not applicable in this scenario. The calculated pressure of 100 kPa is well below this value. - **Option D: 300 kPa**: This is also too high. Similar to option C, it does not reflect the correct calculation based on the given depth and density. ### Common Pitfalls - **Neglecting Atmospheric Pressure**: The question specifies to neglect atmospheric pressure, which is crucial. If atmospheric pressure were included, the total pressure would be higher, but since we are only considering the hydrostatic pressure, we focus solely on the fluid's contribution. - **Misunderstanding Units**: Ensure that you convert between Pascals and kilopascals correctly. Remember that \( 1 \, \text{kPa} = 1000 \, \text{Pa} \). ### Revision Summary - Use the hydrostatic pressure formula \( P = \rho g h \) to calculate pressure at a depth in a fluid. - For water at 10 m depth, with a density of \( 1000 \, \text{kg/m}^3 \) and \( g \approx 9.81 \, \text{m/s}^2 \), the pressure is approximately \( 100 \, \text{kPa} \). - Always check units and conversions when calculating pressure. - Remember to consider whether atmospheric pressure is included in the problem statement.