What is the volume of a rectangular parallelepiped if the areas of its three faces are 6.12.8 cm2?

The volume of a rectangular parallelepiped is calculated by the formula:

V = abc, where abc are sides.

Knowing that the areas of its faces are equal to S1 = 6 cm2, S2 = 12 cm2, S3 = 8 cm2, we can calculate what the sides of a rectangular parallelepiped are equal to.

Knowing the area formula for a rectangle S = ab, we find the sides:

a * b = 6 cm2.

b * c = 12 cm2.

a * c = 8 cm2.

Side a = 6: b; side c = 12: b; side b = (6: b) * (12: b) = 8.

Let’s expand the brackets by multiplying each factor of the first parenthesis by each factor of the second:

6 * 12: b * b = 8.

72: b2 = 8.

b ^ 2 = 72: 8.

b ^ 2 = 9.

b = √9.

b = 3.

Let’s find the rest of the sides:

a * b = 6 => a * 3 = 6 => a = 2.

b * c = 12 => 3 * c = 12 => c = 4.

It turns out that the volume of a rectangular parallelogram is:

V = abc = 2 * 3 * 4 = 24 cm3.