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Le the pressure at the bottom = P1 and volume = V1
Let the pressure at the surface = P2 and volume = V2
Temperature remains constant so
P1V1 = P2V2
Given that: V2 = 8V1
therefore, P1 = 8P2
Pressure = hρg
ρ = density of water
g = acceleration due to gravity
P2 = hρg = 10ρg
P1 = 8(10ρg)
P1 - P2 = 80ρg - 10ρg = 70ρg
From hydrostatics,
P1 - P2 = hρg
70 ρ g = hρg
h = 70 m
Depth of the lake = 70m
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