From a rectangular parallelepiped whose volume is 1024 cm2. cut off the cube

From a rectangular parallelepiped whose volume is 1024 cm2. cut off the cube The length and width of the parallelepiped are equal, and the height is 2 times the width. Find the volume of the remaining part if the edge of the cube is equal to the width of the parallelepiped.

Let’s say that the length of this parallelepiped is x cm.

According to the condition of the problem, the width is equal to the length, that is, also x cm, and the height is 2 times the width, that is, 2 * x cm.

As you know, the volume of a rectangular parallelepiped is equal to the product of its measurements, therefore, we get the equation:

2 * x * x * x = 1024,

х³ = 1024: 2,

x³ = 512,

x = 8 (cm).

The edge of a cube is equal to the width of this parallelepiped, which means that its volume is:

8 * 8 * 8 = 8³ = 512 (cm³).

Thus, the volume of the remaining part of the parallelepiped is:

1024 – 512 = 512 (cm³).