Question

(a) What is Volume?
(b) Write the relationship between the following units:
(i) $hectare$ and $meter{e^2}$ (ii) $metr{e^3}$ and $c{m^3}$ (iii) $metr{e^3}$ and $litre$ (iv) $c{m^3}$ and $mL$ (v) $'acre'$ and $meter{e^2}$

Answer 1

Hint:We have to state the definition of volume. In mathematical expression we consider volume as the product of length, breadth and height. In the second part of the question, we will find out the relationship between the different units as stated in the question.

Complete step by step answer:
(a) Volume is defined as the amount of substance that a surface occupies. In physics, we state volume as the quantity of three-dimensional space that is occupied by a closed surface. For example we can say let us consider a jug that could hold water. So, the volume of the jug can be defined as the amount of the water that the jug can hold. The SI unit of volume is $metr{e^3}$.

(b) The relation between the different units are listed below-
(i) $hectare$ and $meter{e^2}$
$1{\text{ }}Hectare = 10000{\text{ }}metr{e^2}$
(ii) $metr{e^3}$ and $c{m^3}$
$1{\text{ }}c{m^3} = {10^{ - 6}}{\text{ }}{m^3}$
(iii) $metr{e^3}$ and $litre$
$1{\text{ }}{m^3} = {10^3}{\text{ }}litre$
(iv) $c{m^3}$ and $mL$
$1{\text{ }}c{m^3} = 1{\text{ }}mL$
(v) $'acre'$ and $meter{e^2}$
$1{\text{ }}acre = 4046.86{\text{ }}{m^2}$
This is the relation between these units which are stated in the question.

Note:It must be noted that all of them are standard units which are internationally proven. $hectare$ and $meter{e^2}$ are the units for the measurement of area. $metr{e^3}$ and $c{m^3}$and $litre$ are the units of volume. $acre$ is mainly used for the measurement of area of land for commercial purposes.