In a parallelepiped, the length is 36mm, the height is 6 times less than the length, and the width

In a parallelepiped, the length is 36mm, the height is 6 times less than the length, and the width is equal to the arithmetic mean of the length and height. Find the volume of this parallelepiped.

The problem does not indicate which parallelepiped is being considered. We will assume that this is a rectangular parallelepiped.

1. Let’s denote the dimensions of the parallelepiped through: a – length, b – width and c – height.

2. By the condition of the problem, a = 36 mm.

3. Then the height, which is 6 times less than the length, is c = a / 6 = 36/6 = 6 mm.

4. The arithmetic mean of two values is equal to their sum divided by two. Therefore, width b = (a + c) / 2 = (36 + 6) / 2 = 21 mm.

5. The volume V of a rectangular parallelepiped is equal to the product of its measurements. I.e,
V = a * b * c = 36 * 21 * 6 = 4536 mm3.

Answer: the volume of the parallelepiped is 4536 mm3.