What is the volume of a rectangular parallelepiped if the areas of its three faces are 6.12.8 sq.

Let the height, width and length of the parallelepiped be equal to a, b and c.

The areas of the faces can only take on the values: a * b, a * c, b * c.

If the product of the areas of two faces is divided by the third, then we get the square of the length of one of the dimensions:

((a * b) * (a * c)) / bc = a ^ 2;

((a * c) * (b * c)) / ab = c ^ 2;

((a * b) * (b * c)) / ac = b ^ 2.

Dimensions in our case:

a ^ 2 = (6 * 12) / 8 = 9 cm ^ 2; a = 3 cm;

b ^ 2 = (6 * 8) / 12 = 4 cm ^ 2; b = 2 cm;

c ^ 2 = (12 * 8) / 6 = 16 cm ^ 2; c = 4 cm.

V = 3 cm * 2 cm * 4 cm = 24 cm ^ 3.

Answer: 24 cm ^ 3.