Question

A person measures the length, width, height and mass of a metal block with rectangular sides. Which of the following measurements must be used in order to calculate the density of the metal?
A. Mass only
B. Height and mass only
C. Length, width and height only
D. Length, width, height and mass

Answer 1

Hint: The density of a material can be expressed as the ratio of mass of material and its volume. We will apply the formula of volumetric density to obtain the terms required to calculate the density of the given rectangular box.

Formula used:
$\text{Density = }\dfrac{\text{Mass}}{\text{Volume}}$

Complete step by step answer:
The density of a substance is defined as the measurement of its mass per unit volume. The volumetric mass density of a material is the value obtained when mass of the material is divided by the volume of the material.
For calculating the density of an object mathematically, we need to know the value of its mass and its volume.
In case of a rectangular metal block, the volume of the block can be calculated by knowing the values of length, breadth, and height of the block.
${{V}_{block}}=L\times B\times H$
Where,
$L$ is the length of the block
$B$ is the breadth or width of the block
$H$ is the height of the block
For calculating the density of a metal block, we need to apply the formula of density, that is, mass of the block divided by its volume.
Let’s say mass of the rectangular metal block is $M$
Density of a material is given as,
$\text{Density = }\dfrac{\text{Mass}}{\text{Volume}}$
For rectangular metal block,
${{V}_{block}}=L\times B\times H$
Therefore,
$\text{Density of metal block = }\dfrac{\text{Mass of metal block}}{\text{Volume of metal block}}$
Density is represented by the symbol $\rho $
Thus,
${{\rho }_{block}}=\dfrac{{{M}_{block}}}{{{V}_{block}}}$
Putting value of volume of the block in the above equation, we get,
${{\rho }_{block}}=\dfrac{M}{L\times B\times H}$
Therefore, the following measurements must be used in order to calculate the density of the metal:
Mass of metal block
Length of metal block
Width of metal block
Height of metal block
Hence, the correct option is D.

Note:
The density of a material is its internal property; it does not depend upon the shape and size of the material taken. Although, its value can be calculated by using the values of taken mass and given size of a material. Density is the mass per unit volume of an object or a material.