Question

How do you convert \[127c{m^2}\] into square inches, if 1 inch is equal to 2.54 cm?

Answer 1

Hint: Use the relation given in the question that 1-inch length is equivalent to the length 2.54 cm and also use the fact that unit square represents the result of the multiplication of the unit to itself. That is \[uni{t^2} = unit \times unit\].

Complete step by step solution:
We have to convert 127 square centimetre into square inches.
It is known that centimetre (cm) is a unit of length and when we multiply length to length we convert it into units of area. It means multiplication of centimetre to centimetre which is represented by square centimetre \[c{m^2}\] is the unit of area.
\[cm \times cm = c{m^2}\]
We know that inch is also a unit of length and so square inches will be a unit of area.
\[inch \times inch = inc{h^2}\]
It is given in the question that two point five four centimetres is equal to one inch. That is \[1inch = 2.54cm\].
If we square both sides of the equation \[1inch = 2.54cm\], it will still hold true.
\[{\left( {1inch} \right)^2} = {\left( {2.54cm} \right)^2}\]
Simplify the equation as shown below.
\[ \Rightarrow 1inch \times 1inch = 2.54cm \times 2.54cm\]
\[ \Rightarrow 1inc{h^2} = 2.54 \times 2.54c{m^2}\]
\[ \Rightarrow 1inc{h^2} = 6.4516c{m^2}\]
So, we find the result that one square inches is equal to six point four five one six square centimetre.
Divide both sides of the result equation by the number 6.4516 and solve as shown below.
\[ \Rightarrow \dfrac{1}{{6.4516}}inc{h^2} = \dfrac{{6.4516}}{{6.4516}}c{m^2}\]
\[ \Rightarrow 0.155inc{h^2} = 1c{m^2}\]
So, we find the result that one square centimetre is equal to zero point one five-five square inches.
Use this relation to convert \[127c{m^2}\] in square inches by substituting square centimetre to zero point one five-five square inches as shown below.
\[127c{m^2} = 127 \times 0.155inc{h^2}\]
\[127c{m^2} = 19.685inc{h^2}\]
Thus, the area \[127c{m^2}\] in square centimetre can be written as \[19.685inc{h^2}\] in square inches.

Note:
The unit square represents the multiplication of the unit with itself and therefore when we convert one-unit square into another unit square, we use the relation for square unit not the linear unit. To convert the linear unit relations into square unit relations, just square both sides of the equation.