The diagonal of a regular quadrangular prism is 18 cm, and the side of its base is 8 cm. Find the volume of the prism.

The diagonal of a regular quadrangular prism, the side of the base and the diagonal of the side face make up a right-angled triangle.

The diagonal of the prism is the hypotenuse of this triangle, and the base and the diagonal of the side face are its legs.

Let the diagonal of the side face be x cm, then by the Pythagorean theorem we compose the following equation:

18² = 8² + x²,

х² = 18² – 8²,

x² = 324 – 64,

x = √260.

Knowing the diagonal of the side face and the side of the base, we can find its height:

h² + 8² = 260,

h² = 260 – 64,

h = 14.

As you know, the volume of a regular quadrangular prism is equal to the product of the area of ​​its base by the height. We get:

V = 8 * 8 * 14 = 896 cm³.