The cube has a volume that is half the volume of a rectangular parallelepiped.

The cube has a volume that is half the volume of a rectangular parallelepiped. Find the sum of the areas of all the faces of the cube if the dimensions of the rectangular parallelepiped are 3 cm, 3 cm, 6 cm.

First, we find the volume of the rectangular parallelepiped:

1) V1 = abc,

V1 = 3 • 3 • 6 = 54 (cm3) – the volume of the parallelepiped.

Next, we find the volume of the cube, taking into account the condition of the problem:

2) V2 = 54: 2 = 27 (cm3) – cube volume.

Let’s find the length of the edge of the cube using the formula for its volume:

3) V2 = a ^ 3,

27 = a ^ 3,

a = 3 (cm).

It remains to find the surface area of the cube:

4) S = 6 • a ^ 2,

Since, all the faces of the cube are the same squares, and there are exactly 6 of them.

S = 6 • 3 ^ 2 = 6 • 9 = 54 (cm2) – the area of all sides of the cube.

Answer: 54 cm2 is the area of all the faces of the cube.