Question

Why ${{m}^{2}}$ is a derived quantity while m is a fundamental quantity and why $kmole$ is a fundamental quantity?

Answer 1

As a first step, one could read the question well and hence understand that the given ones are the units of certain physical quantities. We are supposed to find the reason due to which these physical quantities are classified under these categories. Now recall the seven fundamental quantities and also the prefixes given to SI units.

Complete answer:
In the question, we are asked as to why is ${{m}^{2}}$ a derived quantity while m a fundamental quantity. Also, we are asked why $kmole$ classified under fundamental quantities.
So, basically, the quantities that could be measured either directly or indirectly are known as physical quantities and they are classified into two categories namely fundamental and derived quantities.
Fundamental quantities are the ones that are independent of the other fundamental quantities and we have 7 fundamental quantities. Whereas, derived quantities that cannot be measured directly and can only be computed, that is, they can only be calculated from more than one measurement.
You may recall that ${{m}^{2}}$is the unit of area and it is given by the product of two length measurements made in metres. Hence, ${{m}^{2}}$is a derived quantity and m is one among the 7 fundamental quantities.
You may recall that mole is the unit in which amount of substance is measured and k (kilo-) is the prefix given to this unit and hence $kmol$is also a unit given to fundamental quantity.

Note: You may have noted that there is a mention of 7 fundamental quantities and they are: Length(m), Mass(kg), time(s), current(A), temperature(K), luminous intensity(cd), amount of substance(mole). Plane angle(radian) and solid angle(steradian) are classified as supplementary quantities.