# If an object has a volume of 10cm^3, what is its volume in mL?

Sep 22, 2016

$1 \cdot m L = 1 \cdot c {m}^{3}$. And thus $10 \cdot c {m}^{3} = 10 \cdot m L$.

#### Explanation:

Now $1 \cdot m L$ $=$ $1 \times {10}^{-} 3 L$

But $1 \cdot c {m}^{-} 3$ $=$ $1 \cdot {\left({10}^{-} 2 m\right)}^{3}$, because $\text{centi} = {10}^{-} 2$

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

But $1 \cdot {m}^{3}$ $=$ ${10}^{3} L$, and thus ${10}^{-} 6 \cdot {m}^{3}$ $=$ ${10}^{-} 6 \times {10}^{3} L$ $=$ ${10}^{-} 3 L$ $=$ $1 \cdot m L$ as required.