Question

100 square millimetres $(m{m^2}) =$ _______square centimetre $(c{m^2})$
A) 100
B) 10
C) 1
D) $0.1$

Answer 1

A metre is equal to 1000 millimetres and a metre is also equal to 100 centimetres. We will use the formula of area of a square to find the area of the square in the units of centimetres

Complete step by step answer
As mentioned in the hint, a metre is equal to 1000 millimetres. So, let us convert the area in question to metres and consequently all the options in metres too, and then we will compare.
So, 100 square millimeters will be equal to
$A = 100\,m{m^2}$ which when converted to units of meters will be
$A = 100 \times {10^{ - 6}}$
$\Rightarrow A = {10^{ - 4}}\,{m^2}$
Hence the corresponding area of the amount given to us in meters will be ${10^{ - 4}}\,{m^2}$ . Now with the information that $1\,cm = 0.01\,m = {10^{ - 2}}\,m$ , we can write:
Now, in option (A), 100 square-centimeters will be equal to $100 \times {10^{ - 4}}\,{m^2}$ or ${10^{ - 2}}\,{m^2}$ which is not equal to the area given in question so option (A) is incorrect.
Now, in option (B), 10 square centimeters will be equal to $10 \times {10^{ - 4}}\,{m^2}$ or ${10^{ - 3}}\,{m^2}$ which is not equal to the area given in question so option (A) is incorrect.
Now, in option (C), 1 square centimeter will be equal to $1 \times {10^{ - 4}}\,{m^2}$ or ${10^{ - 4}}\,{m^2}$ which is equal to the area given in question so option (C) is correct.
Hence the correct choice will be option (C).

Note
We can solve this question without directly knowing the inter-conversions between metre squared and centimetre squared. To do so, we make use of the fact that area is proportional to the square of the units of length and then calculating the relation between meter squared and centimetre squared using the relation between metres and centimetres.