The width of the rectangular parallelepiped is 12 cm, it is 3 times longer, and the height is 3 cm

The width of the rectangular parallelepiped is 12 cm, it is 3 times longer, and the height is 3 cm more than the width. Find the volume of the rectangular parallelepiped.

Let’s denote the length of the rectangular parallelepiped as a, width as b, and height as c.

By condition, b = 12 cm.

From the condition it is known that the length of a given parallelepiped is 3 times its width, therefore:

a = 3 * b;

a = 3 * 12 = 36 (cm).

It is also known that the height of the parallelepiped is 3 cm greater than its width, therefore:

c = b + 3;

c = 12 + 3 = 15 (cm).

The volume of a rectangular parallelepiped is equal to the product of its length and width and height, that is:

V = a * b * c.

Let’s substitute the data on the condition and the found values:

V = 36 * 12 * 15 = 6480 (cm³).

Answer: V = 6480 cm³.