Question

A metal block has a density of 5000 kg per cubic meter and a mass of 15,000 kg. What is its volume?

Answer 1

Taking into account the definition of density, the volume of the metal block is 3 m³.

What is density

Density is defined as the property that matter, whether solid, liquid or gas, has to compress into a given space.

In other words, density is a quantity that allows us to measure the amount of mass in a certain volume of a substance.

Then, the expression for the calculation of density is the quotient between the mass of a body and the volume it occupies:

$density=\frac{mass}{volume}$

From this expression it can be deduced that density is inversely proportional to volume: the smaller the volume occupied by a given mass, the higher the density.

Volume of the metal block

In this case, you know that:

• Density= 5000 $\frac{kg}{m^{3} }$
• Mass= 15000 kg
• Volume= ?

Replacing in the definition of density:

$5000 \frac{kg}{m^{3} } =\frac{15000 kg}{volume}$

Solving:

volume×5000 $\frac{kg}{m^{3} }$= 15000 kg

volume= $\frac{15000 kg}{5000 \frac{kg}{m^{3} }}$

volume= 3 m³

In summary, the volume of the metal block is 3 m³.

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