A cube has a side of length $1.2 \times 10^{-2}\,\text{m}$. Calculate its volume.

Step 1: Identify the given values and formula.

The side length of the cube is given.

$$a = 1.2 \times 10^{-2}\,\text{m}$$

The volume $V$ of a cube is calculated using the side length.

$$V = a^{3}$$

Step 2: Calculate the volume.

Substitute the side length into the volume formula.

$$V = (1.2 \times 10^{-2}\,\text{m})^{3}$$ $$V = 1.728 \times 10^{-6}\,\text{m}^{3}$$

Step 3: Apply significant figures.

Since the side length has $2$ significant figures, the final volume must also be rounded to $2$ significant figures.

$$V \approx 1.7 \times 10^{-6}\,\text{m}^{3}$$

Answer: $1.7 \times 10^{-6}\,\text{m}^{3}$