Calculate the Space Diagonal: Finding the Corner-to-Corner Distance in a 10cm Cube

To find the inner diagonal of a cube where each edge is 10 cm long, we will use the Pythagorean theorem in three dimensions. For a cube with edge length $a$, the formula to find the diagonal $d$ is:

$d = a \sqrt{3}$

In this problem, the edge length $a = 10$ cm. Substituting into the formula gives:

$d = 10 \sqrt{3}$

Calculating $10 \sqrt{3}$, we estimate $\sqrt{3} \approx 1.732$. Thus:

$d \approx 10 \times 1.732 = 17.32$

Rounded to one decimal place (as often required for physical measures), the length of the inner diagonal of the cube is approximately $17.3$ cm.

Therefore, the correct choice is the one that matches this calculation, which is:

$17.3$ cm.