The surface area of a cube is 54 dm2. Find its volume

It is known from the condition that the surface area of the cube is 54 dm ^ 2. And we need to find its volume.

Let’s first recall the formula for calculating the volume of a cube:

V = a ^ 3.

Now we need to find the length of the side edge of the cube. To do this, we will apply the formula to find the surface area of a cube:

S pov. cube = 6a ^ 2.

Let us express the lateral edge from the formula:

a = √ (S / 6).

Substitute values and perform calculations:

a = √ (54/6) = √9 = 3 dm.

We substitute the values into the formula for calculating the volume:

V = 3 ^ 3 = 27 dm ^ 3.