# There is a zinc cube on the floor with a cavity inside. The length of the edge of the cube is a = 50 cm.

There is a zinc cube on the floor with a cavity inside. The length of the edge of the cube is a = 50 cm. The pressure exerted by the cube on the floor is p = 600 Pa. The density of zinc is ρ = 7100 kg / m3. What part of the volume of the cube is occupied by the cavity? Disregard atmospheric pressure.

Given:

a = 50 centimeters = 0.5 meters – the length of the edge of the zinc cube with a cavity inside;

P = 600 Pascal – the pressure exerted by the cube on the floor;

ro = 7100 kg / m3 (kilogram per cubic meter) – zinc density;

g = 10 Newton / kilogram – acceleration due to gravity (rounded off value).

It is required to determine n – what part of the volume of the cube the cavity occupies.

Find the surface area on which the cube rests:

s = a ^ 2 = 0.5 ^ 2 = 0.25 m2.

The force of gravity acting on the cube will be equal to:

F = P * s = 600 * 0.25 = 150 Newtons.

The mass of the cube is:

m = F / g = 150/10 = 15 kilograms.

If there was no cavity in the cube, its volume would be equal to:

V = m / ro = 15/7100 = 0.0021 m3.

The actual volume of the cube is:

Vact = a3 = 0.53 = 0.125 m3.

Then the volume of the cavity is equal to:

Vcavity = V – Vact = 0.125 – 0.0021 = 0.123.

That is, the volume of the cavity occupies a part of the total volume:

n = Vcavity / Vact = 0.123 / 0.125 = 0.984 or 98.4%.

Answer: the volume of the cavity occupies 98.4% of the volume of the cube.

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