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The mass of $3{m^3}$ of cement of density 3000 $kg/{m^3}$ is
A) 1000kg
B) 9000kg
C) 10000kg
D) 90000kg

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Last updated date: 27th Feb 2024
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IVSAT 2024
Answer
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Hint: Here, we will proceed by defining the density of any substance. Then, we will express the density mathematically. Finally, we calculate its mass by using the formula of density. Density is mass per unit volume.

Complete step by step answer:
Density of any material is simply the ratio of the mass of the material to the volume of the material. Mathematically, density of any substance can be expressed as
${\rm{Density}}\left( \rho \right){\rm{ = }}\dfrac{{{\rm{Mass}}\left( {\rm{m}} \right)}}{{{\rm{Volume}}\left( {\rm{V}} \right)}}$
Density is denoted by rho, mass is (m) and volume is (V)
According to given data,
Volume of cement is $ = 3\;{{\rm{m}}^3}$
Density of cement is $ = \;3000\;{\rm{kg/}}{{\rm{m}}^3}$
By using above formula we get,
$3000{\rm{kg/}}{{\rm{m}}^3}\; = \;\dfrac{{{\rm{mass (m)}}}}{{3\;{{\rm{m}}^3}}}$
$ \Rightarrow \;{\rm{mass}}\; = \,3000{\rm{kg/}}{{\rm{m}}^3} \times \;3{{\rm{m}}^3}$ $\therefore \;{\rm{mass = }}\;{\rm{9000 kg}}$

Hence the correct option is (B).

Additional information: Density is a quantitative physical attribute of a material or of a more or less stable mixture. When we take a piece of material, it has some mass and volume. The mass divided by volume is called density, and it depends solely on substance (remains the same for different parts of the same material).

Note: Compared to solid-liquid and gas, the solid has more density and liquid have less density; liquid density exists between solids and gases. For example, wood always floats on water because the wood is less dense than water. The unit of density is ${\rm{kg/}}{{\rm{m}}^3}$.
The dimensional formula of density is derived as, ${\rm{Density}}\left( \rho \right){\rm{ = }}\dfrac{{{\rm{Mass}}\left( {\rm{m}} \right)}}{{{\rm{Volume}}\left( {\rm{V}} \right)}}$
The dimension of mass (m) = [M]
Also, the dimension of volume (V) = $[{L^3}]$
$ \Rightarrow \;\rho \; = \;\dfrac{{{\rm{[M]}}}}{{{\rm{[}}{{\rm{L}}^3}]}} = \left[ {{\rm{M}}{{\rm{L}}^{ - 3}}} \right]$