To solve the problem of finding the height of the boy based on the hydrostatic blood pressure difference, we can use the hydrostatic pressure formula. Let's break down the steps clearly. ### Step 1: Understand the Hydrostatic Pressure Formula The hydrostatic pressure difference (\( \Delta P \)) between two points in a fluid column is given by the formula: \[ \Delta P = \rho g h \] Where: - \( \Delta P \) = pressure difference (in Pascals, or \( \text{N/m}^2 \)) - \( \rho \) = density of the fluid (in \( \text{kg/m}^3 \)) - \( g \) = acceleration due to gravity (in \( \text{m/s}^2 \)) - \( h \) = height difference (in meters) ### Step 2: Identify the Given Values From the problem, we have: - \( \Delta P = 1.65 \times 10^4 \, \text{N/m}^2 \) - \( \rho = 1.1 \times 10^3 \, \text{kg/m}^3 \) - \( g = 10 \, \text{m/s}^2 \) ### Step 3: Rearranging the Formula We need to find the height \( h \). Rearranging the hydrostatic pressure formula gives us: \[ h = \frac{\Delta P}{\rho g} \] ### Step 4: Substitute the Values Now, we can substitute the known values into the rearranged formula: \[ h = \frac{1.65 \times 10^4 \, \text{N/m}^2}{(1.1 \times 10^3 \, \text{kg/m}^3)(10 \, \text{m/s}^2)} \] ### Step 5: Calculate the Denominator First, calculate the denominator: \[ \rho g = (1.1 \times 10^3 \, \text{kg/m}^3)(10 \, \text{m/s}^2) = 1.1 \times 10^4 \, \text{N/m}^3 \] ### Step 6: Calculate the Height Now substitute this back into the equation for \( h \): \[ h = \frac{1.65 \times 10^4 \, \text{N/m}^2}{1.1 \times 10^4 \, \text{N/m}^3} \] Calculating this gives: \[ h = \frac{1.65}{1.1} \, \text{m} = 1.5 \, \text{m} \] ### Conclusion Thus, the height of the boy is **1.5 m**. Therefore, the correct option is **C**. ### Explanation of Other Options - **Option A (0.5 m)**: This is too low for the height calculated based on the pressure difference. It does not satisfy the hydrostatic pressure equation. - **Option B (0.6 m)**: Similar to option A, this value is also too low and does not match the calculated height. - **Option D (2.0 m)**: This value is higher than the calculated height. It would imply a greater pressure difference than what is given. ### Revision Summary - The hydrostatic pressure difference can be calculated using \( \Delta P = \rho g h \). - Rearranging gives \( h = \frac{\Delta P}{\rho g} \). - Substitute the known values carefully to find the height. - The correct height of the boy is **1.5 m**, corresponding to option **C**.