On the table is a zinc cube with a cavity inside. The length of the edge of the cube is 50cm. The pressure exerted

On the table is a zinc cube with a cavity inside. The length of the edge of the cube is 50cm. The pressure exerted by the cube on the floor is 600 Pa. What part of the volume does the cavity occupy?

Given:

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

ro = 7800 kg / m3 – zinc density;

g = 10 m / s2 – acceleration of gravity.

P = 600 Pascal – the pressure that zinc exerts on the table surface.

It is required to determine V1 / V – what part of the volume of the cube is occupied by the volume of the cavity inside the cube.

Find the area of ​​the base of the cube:

S = a * a = 0.5 * 0.5 = 0.25 m2.

Then 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 will be equal to:

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

Let’s find the actual volume of the cube:

V = a3 = 0.53 = 0.125 m3.

Let’s find the volume that the cube should occupy if there was no cavity in it:

V2 = m / ro = 15/7800 = 0.002 m3.

Then the volume of the cavity is equal to:

V1 = V – V2 = 0.125 – 0.002 = 0.123 m3.

V1 / V2 = 0.123 / 0.125 = 0.984.

Answer: the volume of the cavity takes up 0.984 part of the volume of the cube.