Respuesta :
Answer:
The mass of the cube is 420.8 kg.
Explanation:
Given that,
Length of edge = 38.9 cm
Density [tex]\rho= 7.15 \times10^{3}\ kg/m^3[/tex]
We need to calculate the volume of cube
Using formula of volume
[tex]V = 38.9^3[/tex]
[tex]V=0.058863\ m^3[/tex]
We need to calculate the mass of the cube
Using formula of density
[tex]\rho = \dfrac{m}{V}[/tex]
[tex]m = V\times\rho[/tex]
[tex]m =0.058863\times7.15 \times10^{3}[/tex]
[tex]m=420.8\ kg[/tex]
Hence, The mass of the cube is 420.8 kg.
Taking into account the definition of density, the cube's mass is 420.846 kg.
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:
[tex]density=\frac{mass}{volume}[/tex]
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.
Cube's mass
In this case, you know that:
- Density= 7.15×10³ [tex]\frac{kg}{m^{3} }[/tex]
- Volume of a cube= Length³= (38.9 cm)³= (0.389 m)³= 0.05886 m³
Replacing in the definition of density:
[tex]7.15x10^{3}\frac{kg}{m^{3} } =\frac{mass}{0.05886 m^{3} }[/tex]
Solving:
mass= 7.15×10³ [tex]\frac{kg}{m^{3} }[/tex] ×0.05886 m³
mass= 420.846 kg
In summary, the cube's mass is 420.846 kg.
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