The pressure at the bottom of a tank containing a liquid does not depend on

The correct answer is Area of the bottom surface.

Step-by-step Explanation:

1. Understanding Hydrostatic Pressure:
The pressure exerted by a static liquid column at a certain depth is known as hydrostatic pressure. Let us derive the formula for this pressure to see which physical quantities it depends on.

2. Derivation of the Formula:
Consider a tank containing a liquid of density $\rho$ (rho) filled up to a height $h$. Let the cross-sectional area of the bottom surface of the tank be $A$.

The volume ($V$) of the liquid in the tank is given by:
$V=A\times h$

The mass ($m$) of the liquid is the product of its volume and density:
$m=V\times \rho =A\times h\times \rho$

The force ($F$) exerted by this liquid weight on the bottom surface of the tank is:
$F=m\times g=A\times h\times \rho \times g$
where $g$ is the acceleration due to gravity.

Pressure ($P$) is defined as force per unit area:
$P=\frac{F}{A}=\frac{A\times h\times \rho \times g}{A}$

Simplifying the equation by cancelling the area $A$ from the numerator and the denominator, we get:
$P=h\times \rho \times g$

3. Analyzing the Dependencies:
From the derived equation $P=h\rho g$, we can see that the hydrostatic pressure at the bottom of the tank depends on:
- The height of the liquid column ($h$)
- The density/nature of the liquid ($\rho$)
- The acceleration due to gravity ($g$)

Because the area term ($A$) cancels out during the derivation, the pressure is entirely independent of the area of the bottom surface of the container.