The total surface area of a cube is $294{\text{cm}}^2$. What is the length of its diagonal?

Let the side length of the cube be $a$.
The total surface area of a cube is given by the formula:

$$\text{Total Surface Area}=6a^2$$

$$294=6a^2⟹a^2=\frac{294}{6}=49⟹a=7\text{cm}$$

The length of the diagonal of a cube is given by $a\sqrt{3}$.

$$\text{Length of diagonal}=7\sqrt{3}\text{cm}$$