Question

A cork has a volume of $25c{m^3}$ .The density of cork is $0.25gc{m^{ - 3}}$ . Find the mass of cork.

Answer 1

Density is a measure of mass per volume. The density of material shows the denseness of that material in a specific given area. The formulae used in the solution are given here.
Density $\rho = \dfrac{m}{V}$ where $m$ is the mass and the volume is $V$ .

Complete Step by Step Solution
A material’s density is defined as its mass per unit volume. Density is essentially a measurement of how tightly matter is packed together. It is represented by $\rho$ . It is a unique physical property for a particular object. The principle of density was discovered by the Greek scientist Archimedes.
Mathematically, density $\rho = \dfrac{m}{V}$ where $m$ is the mass and the volume is $V$ .
The average density of an object equals its total mass divided by its total volume. An object made from a comparatively dense material (such as iron) will have less volume than an object of equal mass made from some less dense substance (such as water).
It has been given that a cork has a volume of $25c{m^3}$ and the density of cork is $0.25gc{m^{ - 3}}$ .
Thus, volume $V = 25c{m^3}$ and density $\rho = 0.25gc{m^{ - 3}}$ .
Now, substituting these values in the equation stated above, we get,
$0.25 = \dfrac{m}{{25}}$ .
Simplifying the equation,
$m = 0.25 \times 25$
$\Rightarrow m = 6.25g$
Hence the mass of the cork is $6.25g$ .

Note:
Though SI unit of density is ${{kg} \mathord{\left/ {\vphantom {{kg} {{m^3}}}} \right. } {{m^3}}}$ , for convenience we use ${g \mathord{\left/ {\vphantom {g {c{m^3}}}} \right. } {c{m^3}}}$ for solids, ${g \mathord{\left/ {\vphantom {g {ml}}} \right. } {ml}}$ for liquids, and ${g \mathord{\left/ {\vphantom {g L}} \right. } L}$ for gases. Density can be explained as the relationship between the mass of the substance and the volume it takes up. In a qualitative term, it shows how heavy an object is at constant volume. Different substances have different density, which means the same volume of different substances weigh differently.