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

Hint: 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.