Question

How do you convert \[{m^3}\] to \[c{m^3}\].

Answer 1

Hint: In this question, the concept of the conversion factor is used. As we know that meter cube and centimeter cube are the measuring units of the volume. We will use the conversion of length that is one meter is equal to $100$ centimeter.

Complete step by step answer:
In this question, we need to convert the volume units that are from meter cube to centimeter cube.
First, we will talk about cubic centimeters and cubic meters. Cubic centimeters are denoted by \[c{m^3}\] and cubic meters are denoted by \[{m^3}\].
We know that the one-meter is equal to a hundred centimeters.
Then we will get,
\[1\,meter = 100\,centimeter\]
Now, we calculate the volume of the cube by raising the length of its side to the power of three.
Then,
\[1\,{m^3} = 1m \times 1m \times 1m\]
We have to notice that, we can write \[{\text{1}}m\] as \[{\text{100}}cm\],
Put this value in above equation,
Then we get,
\[1\,{m^3} = 100cm \times 100cm \times 100cm\]
We can write this equation as below.
\[ \Rightarrow 1\,{m^3} = \left( {100 \times 100 \times 100} \right)\left( {cm \times cm \times cm} \right)\]
After simplification we get,
\[\therefore 1\,{m^3} = 1000000c{m^3}\]

Therefore, one cubic meter is equal to \[1000000\] cubic centimetre that is \[1{m^3} = {10^6}c{m^3}\].

Note: Let’s know about cubic centimetre and cubic meter.
Cubic centimeter: As we know cubic centimeter is the quantity of a cube of size one centimeter. More often it is referred to as a milliliter it is a thousand of a litter.
Cubic meter: As we know that it is a metric unit of volume commonly utilized in expressing concentrations of a chemical during a volume of air. One cubic meter is equal to $35.3$ cubic feet or $3$ cubic yards. One cubic meter also equals $1000$ litter or one million cubic centimeters.