A cube has a side of length 1.2 x 10⁻² m. Calculate its volume.

The correct option is 1.7x10⁻⁶ m³.

Step-by-Step Explanation:

To find the volume of a cube, we use the standard formula for the volume of a cube:
$V=s^3$
where $V$ represents the volume and $s$ represents the length of a side of the cube.

Given in the problem:
Side length, $s=1.2\times {10}^{-2}\text{m}$
Note that the value is given with two significant figures (1.2).

Substitute the value of $s$ into the formula:
$V={(1.2\times {10}^{-2}\text{m})}^3$
$V={\left(1.2\right)}^3\times {\left({10}^{-2}\right)}^3{\text{m}}^3$
$V=1.728\times {10}^{-6}{\text{m}}^3$

Applying Significant Figures Rules:
When multiplying or raising measurements to a power, the final result must be rounded to the same number of significant figures as the measurement with the fewest significant figures.
Since the side length $1.2\times {10}^{-2}\text{m}$ has 2 significant figures, we must round our calculated volume to 2 significant figures:
$1.728\times {10}^{-6}{\text{m}}^3\Rightarrow 1.7\times {10}^{-6}{\text{m}}^3$

Thus, the volume of the cube is $1.7\times {10}^{-6}{\text{m}}^3$.