Final answer:
The correct answer is (c) 3h.
Step-by-step explanation:
To find the depth of the lake, we can use the equation for pressure in a fluid of constant density. The pressure at a depth in a fluid is equal to the pressure of the atmosphere plus the pressure due to the weight of the fluid.
In this case, the pressure at half the depth of the lake is equal to 2/3 the pressure at the bottom of the lake.
We can set up the equation as follows:
Pressure at half the depth = Pressure at the bottom of the lake
Pressure at half the depth = Pressure of the atmosphere + Pressure due to the weight of the water
2/3 * Pressure at the bottom = Pressure of the atmosphere + Pressure due to the weight of the water
Solving for the depth, we find:
Depth of the lake = 3 * Height of the atmosphere
Therefore, the correct answer is 3h.