The volume of a cube is 3375 $$cm^{3}$$. What is the length of the longest rod that can be placed in this cube?

Let's assume the length of each side of the cube is 'a' cm.

The volume of a cube is 3375 $$cm^{3}$$.

volume of a cube = $$a^3$$

$$a^3 = 3375$$

$$a^3 = 15^3$$

a = 15 cm

As we know that the longest rod that can be placed in this cube is equal to its diagonal.

diagonal = $$\sqrt{\ 3}\times a$$

= $$\sqrt{\ 3}\times 15$$

= $$15\sqrt{\ 3}$$

So the length of the longest rod that can be placed in this cube is $$15\sqrt{\ 3}$$ cm.