Answer:
The depth is 5.15 m.
Explanation:
Lets take the depth of the pool = h m
The atmospheric pressure ,P = 101235 N/m²
The area of the top = A m²
The area of the bottom = a m²
Given that A= 1.5 a
The force on the top of the pool = P A
The total pressure on the bottom = P + ρ g h
ρ =Density of the water = 1000 kg/m³
The total pressure at the bottom of the pool = (P + ρ g h) a
The bottom and the top force is same
(P + ρ g h) a = P A
P a +ρ g h a = P A
ρ g h a = P A - P a
[tex]h=\dfrac{P ( A-a)}{\rho g a}[/tex]
[tex]h=\dfrac{P ( 1.5 a-a)}{\rho g a}[/tex]
[tex]h=\dfrac{P ( 1.5- 1)}{\rho g}[/tex]
[tex]h=\dfrac{101235 ( 1.5- 1)}{1000\times 9.81}\ m[/tex]
h=5.15 m
The depth is 5.15 m.
