To solve this problem, we need to find the height $h$ using the formula for hydrostatic pressure:

$p_h = \rho \cdot g \cdot h$

Where:

• $p_h$ is the hydrostatic pressure, given as $17773.5$ Pa.
• $\rho$ is the density of the fluid, given as $867 \, \text{kg/m}^3$.
• $g$ is the acceleration due to gravity, given as $10 \, \text{N/kg}$.

We need to rearrange the equation to solve for $h$:

$h = \frac{p_h}{\rho \cdot g}$

Now plug in the given values:

$h = \frac{17773.5}{867 \times 10}$

$h = \frac{17773.5}{8670}$

$h \approx 2.05 \, \text{m}$

Since the problem asks for the height in centimeters, convert meters to centimeters:

$h \approx 205 \, \text{cm}$

Thus, the height $h$ is approximately $205 \, \text{cm}$, rounded to one decimal place, it is $205.0 \, \text{cm}$.

Would you like more details or have any questions?

Here are 5 related questions to consider:

1. What is hydrostatic pressure and how is it derived?
2. How does fluid density affect hydrostatic pressure?
3. What units are commonly used for measuring pressure, density, and height?
4. How does gravitational acceleration vary on different planets?
5. Why is the unit conversion necessary in this type of calculation?

Tip: When solving for variables in physics, always ensure the units are consistent throughout the equation to avoid calculation errors.