To determine the length of the diagonal in a cuboid with side lengths of $3 \, \text{cm}$, $4 \, \text{cm}$, and $5 \, \text{cm}$, we can use the formula for the space diagonal, which is derived from the Pythagorean theorem. The formula is given by:

$d = \sqrt{a^2 + b^2 + c^2}$

In this formula, $a$, $b$, and $c$ represent the lengths of the cuboid’s sides. For our specific case, the side lengths are $3 \, \text{cm}$, $4 \, \text{cm}$, and $5 \, \text{cm}$. Substituting these values into the formula, we have:

$d = \sqrt{3^2 + 4^2 + 5^2}$

First, we calculate the squares of each side:

$3^2 = 9$ $4^2 = 16$ $5^2 = 25$

Next, we sum these squared values:

$9 + 16 + 25 = 50$

Finally, we take the square root of this sum to find the diagonal length:

$d = \sqrt{50}$

Thus, the length of the diagonal is $\sqrt{50} \, \text{cm}$. If you prefer a decimal approximation, $\sqrt{50}$ is approximately $7.07 \, \text{cm}$. This method allows you to accurately calculate the diagonal length of any cuboid by taking into account all three dimensions.