Each side a cube is measured to be 7.203 m. The volume of the cube up to appropriate significant figures is

The correct option is 373.7.

Step-by-step explanation:

1. Identify the given value and its significant figures:
The measured side length of the cube is:
$s=7.203\text{m}$
The number $7.203$ has four significant figures (7, 2, 0, and 3).

2. Calculate the volume of the cube:
The formula for the volume ($V$) of a cube with side length $s$ is:
$V=s^3$
Substituting the measured side length into the formula:
$V={\left(7.203\text{m}\right)}^3=\mathrm{373.714754...}{\text{m}}^3$

3. Apply the rules of significant figures for multiplication:
According to the rules of arithmetic operations with significant figures, the final result of a multiplication or power calculation should contain no more significant figures than the original measurement with the least number of significant figures.
Since the side length was measured to 4 significant figures, the final volume must also be rounded to 4 significant figures.

4. Rounding off:
Rounding $\mathrm{373.714754...}$ to four significant figures, we look at the fifth digit (which is 1, less than 5). Thus, we round down.
$V\approx 373.7{\text{m}}^3$