You drop an irregular piece of metal into a container partially filled with water and measure that the water level rises 4.8 centimeters. The square base of the container has a side length of 8 centimeters. You measure the mass of the metal to be 450 grams. What is the density of the metal?

Density = 1464.8kg/m3

the density of the metal is 1464.8kg/m^3

Explanation:

Given;

Mass m = 450g

Density = Mass/Volume = m/V

Volume V = change in height * base area = ∆h * A

∆h = 4.8cm

A = 8*8 = 64cm^2

V = 4.8*64 = 307.2cm^3

Density = 450g/307.2cm^3

Density = 1.4648g/cm^3

Density = 1.4648 * 1000kg/m^3

Density = 1464.8kg/m3

the density of the metal is 1464.8kg/m^3

1464.84 kg/m³

Explanation:

Density = mass/volume.

D = m/v ... Equation 1

But from Archimedes principle,

every object immersed in water will displaced an amount of water equal to its own volume

Therefore,

v = v' ... Equation 2

Where v = volume of the irregular object, v' = volume of water displaced.

Since the base of the container is a square,

Then,

v' = L² (d) ... Equation 3

Where L = length of the square base of the container, d = rise in water level.

Substitute equation 3 into equation 1

D = m/L²d ... Equation 4

Given: m = 450 g = 0.45 kg, L = 8 cm = 0.08 m, d = 4.8 cm = 0.048 m

Substitute into equation 4

D = 0.45 / (0.08²*0.048)

D = 0.45/0.0003072

D = 1464.84 kg/m³