The lengths of the sides of a cuboid are y+4, y+2, 2y+1, and y+1. Find the value of y and the volume of the cuboid.

From the diagram, the length is $y+4 \text{ cm}$, the height is $y+2 \text{ cm}$.
The width (or depth) of the cuboid is labeled with two expressions: $2y+1 \text{ cm}$ and $y+1 \text{ cm}$. Since these represent the same physical dimension, they must be equal.

Subtract $y$ from both sides:

Subtract 1 from both sides:

The value of $y$ is:

Length ($l$) $= y+4 = 0+4 = 4 \text{ cm}$
Width ($w$) $= 2y+1 = 2(0)+1 = 1 \text{ cm}$ (or $y+1 = 0+1 = 1 \text{ cm}$)
Height ($h$) $= y+2 = 0+2 = 2 \text{ cm}$

The volume of the cuboid is: