Question

One cm is equal to 10 mm. How many squares mm are there in one square cm?
$
  (a){\text{ 10sq mm}} \\
  (b){\text{ 20sq mm}} \\
  (c){\text{ 100sq mm}} \\
  (d){\text{ 1000sq mm}} \\
$

Answer 1

Hint – In this question the conversion of cm to mm is given to us, we need to find the relation between one square mm and one square cm simply use the given relation and square both sides to obtain the conversion in desired form.

Complete step-by-step answer:
It is given that one cm is equal to 10 mm.
$ \Rightarrow 1{\text{ cm}} = 10{\text{ mm}}$………………. (1)
Now we have to find out how many squares mm are there in one square cm.
So, squaring on both sides in equation (1) we have,
$ \Rightarrow {\left( {1{\text{ cm}}} \right)^2} = {\left( {10{\text{ mm}}} \right)^2}$
$ \Rightarrow \left( {1{\text{ cm}}} \right) \times \left( {1{\text{ cm}}} \right) = \left( {10{\text{ mm}}} \right) \times \left( {10{\text{ mm}}} \right)$
$ \Rightarrow \left( {1 \times 1} \right){\text{ c}}{{\text{m}}^2} = \left( {10 \times 10} \right){\text{ m}}{{\text{m}}^2}$
$ \Rightarrow 1{\text{ c}}{{\text{m}}^2} = 100{\text{ m}}{{\text{m}}^2}$
Or it is also written as
1 sq. cm = 100 sq. mm
So, option (c) is correct.

Note – Whenever we face such types of questions the key concept is simply to have the understanding of the basic conversion unit system. If a given relation is known then its square relation could easily be obtained by just performing simple algebraic operations. This will help you get on the right track to reach the solution.