The sum of the lengths of all the edges of a rectangular parallelepiped is 196 cm.

The sum of the lengths of all the edges of a rectangular parallelepiped is 196 cm. Calculate the volume of a parallelepiped if its two dimensions are 11 cm and 21 cm.

Since the sum of the lengths of all the edges of a rectangular parallelepiped = 196 cm, and two of its dimensions are also known, we compose an equation, taking the unknown dimension for x:

4x + 4 * 11 + 4 * 21 = 196;

We solve the equation:

4x = 196 – 44 – 84 = 68;

x = 68/4 = 17 (cm);

The volume of the parallelepiped will be equal to the product of its three dimensions:

11 * 21 * 17 = 3927 cm3.