The sides of the base of the rectangular parallelepiped are 6 and 8cm, and the diagonal

The sides of the base of the rectangular parallelepiped are 6 and 8cm, and the diagonal of the smaller side face is 10cm. Find the volume of the parallelepiped.

Let us determine what the area of the base of our parallelepiped will equal, when from the condition of the problem we know that the sides of the base are 6 and 8 centimeters, respectively:

6 * 8 = 48.

Let us determine how many centimeters the length of the third dimension, our parallelepiped, will correspond to, when from the condition of the task we know that the diagonal of the smaller face is 10 centimeters:

6 <8;

√ (10 ^ 2 – 6 ^ 2) = √ (100 – 36) = 64 = 8.

Determine the volume of the parallelepiped:

48 * 8 = 384.

Answer: The volume is 384 cm3.