To determine the length of the space diagonal in a cuboid with dimensions $2 \, \text{cm}$, $3 \, \text{cm}$, and $6 \, \text{cm}$, we can use the formula derived from the Pythagorean theorem in three dimensions. The formula is given by:

where $a$, $b$, and $c$ represent the lengths of the cuboid’s sides. For our cuboid, the dimensions are $a = 2 \, \text{cm}$, $b = 3 \, \text{cm}$, and $c = 6 \, \text{cm}$.

First, we calculate the squares of each dimension:

Next, we sum these squared values:

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

Therefore, the space diagonal of the cuboid measures $7 \, \text{cm}$. This diagonal represents the longest straight line that can be drawn within the cuboid, extending from one vertex to the opposite vertex. Understanding how to compute this diagonal is valuable in various applications, such as determining the maximum length of an object that can be accommodated within a given box.