# How many cm^3 in a 10*m^3 volume?

Feb 19, 2016

$1$ $c {m}^{3}$ $=$ $1 \times {\left({10}^{-} 2 \cdot m\right)}^{3}$. There are thus ${10}^{7}$ $c {m}^{3}$ in a $10$ ${m}^{3}$ volume.

#### Explanation:

The $\text{centi}$ prefix means ${10}^{-} 2$.

So $1$ $c {m}^{3}$ $=$ ${\left(1 \times {10}^{-} 2 \cdot m\right)}^{3}$ $=$ $\left(1 \times {10}^{-} 2 \cdot m \times 1 \times {10}^{-} 2 \cdot m \times 1 \times {10}^{-} 2 \cdot m\right)$$=$ $1 \times {10}^{-} 6 \cdot {m}^{3}$.

Thus there are 1 million $c {m}^{3}$ in a cubic metre. Do you agree? All I have done is expanded the prefix $\text{centi}$ using the cubic exponent. Since, there are $1$ $m i l l i o n$ $c {m}^{3}$ in a cubic metre, there are $10 \times {10}^{7}$ $c {m}^{3}$ in a $10$ ${m}^{3}$ volume.

The conversion factor is ${10}^{6}$ $c {m}^{3} {m}^{-} 3$