The diagonal of the cube is 3√3. Find the volume of the cube.

It is known from the condition that the diagonal of the cube is equal to 3√3. And we need to find the volume of the cube.

Let’s start by recalling the formula for calculating the volume of a cube:

V = a ^ 3;

To calculate the volume of a cube, we need to know the length of its face. To do this, we can proceed as follows – recall the formula for calculating the side of a cube through the diagonal.

The formula looks like this:

d = a√3; We express the side from the formula:

a = d / √3.

Substitute the values and calculate:

a = 3√3 / √3 = 3.

Let’s calculate the volume:

V = 3 ^ 3 = 27.