Question

Дан куб. Три плоских разреза, сделанные параллельно граням куба, разделили его на 8 кирпичей (параллелепипедов). Их покрасили в шахматном порядке. Объёмы чёрных кирпичей оказались равны 1, 6, 8, 12. Найдите объёмы белых кирпичей. (Введите четыре числа в любом порядке, через запятую.)​

Answer 1

Ответ:

Рассмотрим две противоположные грани куба, например, верхнюю и нижнюю. ... Поэтому четыре тетраэдра, имеющие грани в верхнем (нижнем) основании куба, не могут заполнить весь исходный куб. ... Это дает три тетраэдра.

Answer 2

Problem Analysis

We are given a cube that has been divided into 8 bricks (parallelepipeds) by three parallel plane cuts. These bricks have been painted in a chessboard pattern, with some bricks painted black. We are given the volumes of the black bricks and need to find the volumes of the white bricks.

Solution

Let's assume the volume of a black brick is represented by x and the volume of a white brick is represented by y.

Since the cube has been divided into 8 bricks, we have a total of 8 bricks. Out of these 8 bricks, we know the volumes of 4 black bricks: 1, 6, 8, and 12. The remaining 4 bricks are white.

To find the volumes of the white bricks, we need to subtract the volumes of the black bricks from the total volume of the cube.

The total volume of the cube can be calculated by summing the volumes of all 8 bricks. Since the cube is divided into 8 equal bricks, the volume of each brick is equal to one-eighth of the total volume of the cube.

Let's represent the total volume of the cube as V. Therefore, the volume of each brick is V/8.

Now, we can set up the following equation to find the volumes of the white bricks:

4y = V - (1 + 6 + 8 + 12)

Simplifying the equation, we get:

4y = V - 27

To find the value of y, we need to know the value of V. Unfortunately, the value of V is not provided in the question. Therefore, we cannot determine the exact volumes of the white bricks without additional information.

However, if we assume that the total volume of the cube is a positive integer, we can find the possible values of y by substituting different values of V into the equation and solving for y.

Please provide the value of the total volume of the cube (V) so that we can calculate the volumes of the white bricks.