The width of a rectangular parallelepiped is 10.2 \ 3cm, its length is 1.7 \ 8 times its width, and its height

The width of a rectangular parallelepiped is 10.2 \ 3cm, its length is 1.7 \ 8 times its width, and its height is 15% of its length. Calculate the volume of the parallelepiped.

1) Volume of a rectangular parallelepiped:

V = a * b * c, where a is the length of the parallelepiped (a = 1 7/8 b), b is the width of the parallelepiped (b = 10 2/3 cm), c is the height of the parallelepiped (c = 15% a).

2) Calculate the length:

a = 1 7/8 b = 1 7/8 * 10 2/3 = (1 * 8 + 7) / 8 * (10 * 3 + 2) / 3 = 15/8 * 32/3 = (3 * 5 ) / 8 * (4 * 8) / 3 = 5 * 4 = 20 cm.

3) Calculate the height:

c = 15% a = 0.15 * 20 = 3 cm.

4) Let’s calculate the volume:

V = a * b * c = 20 * 32/3 * 3 = 20 * 32 = 640 cm3.

Answer: The volume of a rectangular parallelepiped is 640 cm3.