Find the diagonal of a cube that has a surface area of 18.

First, we note that all the faces of the y cube (and their y cube is 6) are equal to each other. Therefore, the area of one face is equal to:

S = 18: 6 = 3 (units).

Since the sides of the cube are squares, then, therefore, the side of this square will be equal to:

a ^ 2 = 3;

a = 3 ^ 1/2.

Now you should derive the formula for determining the diagonal of the cube. T. to. for the diagonal of a parallelepiped there is the following formula:

d ^ 2 = a ^ 2 + b ^ 2 + c ^ 2,

Then for a cube it looks like:

d ^ 2 = 3 * a ^ 2.

Then:

d ^ 2 = 3 * (31/2) ^ 2 = 3 * 3 = 9;

d = 91/2 = 3 (units).

Answer: d = 3.