Question

By converting the \[5.6{\text{ }}{{\text{m}}^2}\] into \[{\text{c}}{{\text{m}}^2}\], the answer will be
A) \[0.0056{\text{ c}}{{\text{m}}^2}\]
B) \[5600{\text{ c}}{{\text{m}}^2}\]
C) \[56000{\text{ c}}{{\text{m}}^2}\]
D) \[560{\text{ c}}{{\text{m}}^2}\]

Answer 1

Hint:
We are required to convert \[5.6{\text{ }}{{\text{m}}^2}\] into \[{\text{c}}{{\text{m}}^2}\]. To solve this question, we need to know the relationship between the meter and centimeter. Based on the relationship between the two quantities we will perform our required conversion.

Complete step by step solution:
The metric system is used for the measurement of the length.
We know that Meter is a unit for measuring the length of any object. It is the standard unit of length. It is denoted by the symbol \[{\text{m}}\].
On the other hand, the centimeter is a smaller unit of length. It is denoted by the symbol \[{\text{cm}}\].
Now, we know that \[1{\text{m}} = 100{\text{cm}}\].
Using the above formula, we will proceed with our required conversion.
Now we know that \[5.6{\text{ }}{{\text{m}}^2}\] can be written as follows –
\[5.6{\text{ }}{{\text{m}}^2} = 5.6 \times 1{\text{m}} \times 1{\text{m}}\]
Since we are required to write this in \[{\text{c}}{{\text{m}}^2}\], we will substitute \[1m\] with \[100cm\] in the above equation. On doing so we get
\[5.6{\text{ }}{{\text{m}}^2} = 5.6 \times 100cm \times 100cm\]
On multiplying the terms, we get,
\[5.6{\text{ }}{{\text{m}}^2} = 5.6 \times 100{\text{ cm}} \times 100{\text{ cm}} = 56000{\text{ c}}{{\text{m}}^2}\]
Thus, \[5.6{\text{ }}{{\text{m}}^2}\] converted into \[{\text{c}}{{\text{m}}^2}\] is \[56000{\text{ c}}{{\text{m}}^2}\].

Hence, the correct answer is option (C).

Note:
The metric system has the following standard units for physical conversion.
These units are as follows –
Kilometer, Hectometer, Decameter, Meter, Decimeter, Centimeter, Millimeter
Even though there are some more units too, these units are most commonly used in practice for the physical measurement of things.
The unit at the top represents the Biggest quantity in this table, whereas, the unit at the bottom of the table represents the smallest unit. The units move from the top to bottom of the table in a difference of 10. Thus, whenever we move down the table from one unit to another, we multiply the multiple of 10 that is equal to the number of places we have jumped.
For example – When we move from Kilometer to Meter, we jump three places, so
\[1{\text{km}} = 1000{\text{m}}\]
Similarly, whenever we move up the table from one unit to another, we divide the multiple of 10 that is equal to the number of places we have jumped.
For example – When we move from Millimeter to Meter, we jump three places, so we can write \[1{\text{mm}} = \dfrac{1}{{1000}}{\text{m}}\].