Question

A cube of aluminum has a mass of 500g. What will be the mass of a cube of magnesium of the same dimensions?
(Density of aluminum is 2.7g/ml)

Answer 1

The mass of a cube of magnesium : 322.2 g

Further explanation

Density is a quantity derived from the mass and volume

Density is the ratio of mass per unit volume

The unit of density can be expressed in g / cm³ or kg / m³

Density formula:

$\large{\boxed {\bold {\rho~=~ \frac {m} {V}}}}$

ρ = density , g / ml

m = mass , g

v = volume , ml

mass of aluminum = 500 g

density of aluminium = 2.7 g/ml

there is data that needs to be added⇒ density of magnesium : 1.74 g/ml

the same dimensions = the same volume

• volume of aluminum

$\tt V=\dfrac{m}{\rho}\\\\V=\dfrac{500}{2.7}=185.19~ml$

• mass of magnesium

V magnesium = V aluminum

$\tt m=\rho\times V\\\\m=1.74\times 185.19\\\\m=\boxed{\bold{322.2~g}}$

Answer 2

The cube of same dimensions of magnesium and aluminum have same volume. The mass of cube of magnesium has been 321.85 grams.

What is density?

The density has been given as the mass of substance per unit volume. The density of aluminum cube has mass 500 grams, and density 2.7 g/mL. The volume of the aluminum cube has been:

$\rm Density=\dfrac{Mass}{Volume}\\\\2.7\;g/mL=\dfrac{500\;g}{Volume} \\\\Volume=185.18\;mL$

The volume of the magnesium and aluminum cube has been the same. The density of magnesium has been 1.735 g/mL. Thus, the mass of Mg cube has been given as:

$\rm 1.738\;g/mL=\dfrac{Mass}{185.18\;mL}\\\\ Mass=321.85\;g$

Thus, the mass of magnesium cube has been 321.85 grams.

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