A cube-shaped vessel filled with water. Find the water pressure at the bottom if the water mass is 27 g.

Let’s translate given in the SI system:
m = 27 g = 0.027 kg

According to Pascal’s law:
The hydrostatic pressure inside the liquid at any depth does not depend on the shape of the vessel in which the liquid is located, and is equal to the product of the density of the liquid, the acceleration of gravity and the depth at which the pressure is determined:
P = ρ * g * h, where ρ is the density of the liquid, g is the free fall acceleration of a body raised above the Earth g = 9.8 m / s2, h is the depth of immersion in the liquid.
According to the reference book, water density ρ = 1000 kg / m³

Let’s write the formula for determining the mass, through the density:
m = ρ * V, where V is the volume of the liquid.
We have a vessel in the shape of a cube, which means its volume:
V = a³ = h³
Substitute this expression into the formula for the mass of the liquid:
m = ρ * V = ρ * h³
Find h from this expression, and substituting the numbers, calculate it:
h = (m / ρ) ^ (1/3) (cubic root of (m / ρ))
h = (0.027 / 1000) ^ (1/3) = 0.03 m.
Substitute the numbers into the formula to determine the pressure:
P = ρ * g * h = 1000 * 10 * 0.03 = 300 Pa

Answer: the water pressure at the bottom is 300 Pa.



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