Volume of a Orthohedron: Using Pythagoras' theorem

To find the length of the diagonal $AC$ on a cuboid, we will use the Pythagorean theorem twice:

• Step 1: Calculate $AB$, the diagonal of the face of the cuboid:

We assume the cuboid's known dimensions, with width $8 \, \text{cm}$ and height $4 \, \text{cm}$. Assume $l$ for one dimension along the base.

Since $AB = \sqrt{w^2 + l^2}$, solving for AB means understanding both directions. As the length isn't given, we solve specifically for vertically so $AC$ depends on full volume space:

• Step 2: Calculate diagonal $AC$:

$AC = \sqrt{AB^2 + \text{height}^2} = \sqrt{8^2 + 4^2} = \sqrt{64 + 16} = \sqrt{80} \, \text{cm}$

In this way, we determine the length of diagonal $AC$ is $\sqrt{80}$ cm.

The correct choice corresponding to this calculation is Choice 3: $\sqrt{80}$ cm.