Question

Умоляю помогите это олимпиада. У прямоугольника параллелепипеда объемом 512 см в кубе уменьшили длину в 4 раза а ширину в 2 раза. В результате получился куб объем которого на 448 см в кубе меньше параллелепипеда. Найти площадь 1 грани куба.

Answer 1

512-448=64см³-объем куба
∛64=4см- ребро куба
4²=16см²-площадь 1 грани куба.

информация об изменении длины, ширины-избыточна

Answer 2

I can help you with your math problem.

According to Google Translate, your question is:

Answer in detail. I beg you to help this is an Olympiad. The volume of a rectangular parallelepiped with a volume of 512 cm in a cube was reduced by 4 times in length and by 2 times in width. As a result, a cube was obtained, the volume of which is 448 cm in a cube less than a parallelepiped. Find the area of 1 face of the cube.

To solve this problem, we need to find the dimensions of the original parallelepiped and the resulting cube. Let the length, width and height of the parallelepiped be l, w and h respectively. Then, we have the following equations:

- The volume of the parallelepiped is 512 cm³: $$l \times w \times h = 512$$ - The length of the parallelepiped is reduced by 4 times: $$\frac{l}{4}$$ - The width of the parallelepiped is reduced by 2 times: $$\frac{w}{2}$$ - The height of the parallelepiped remains the same: $$h$$ - The volume of the cube is 448 cm³ less than the volume of the parallelepiped: $$\left(\frac{l}{4}\right) \times \left(\frac{w}{2}\right) \times h = 512 - 448$$

Simplifying the last equation, we get: $$\frac{l \times w \times h}{8} = 64$$

Substituting the first equation, we get: $$\frac{512}{8} = 64$$

Solving for h, we get: $$h = 8$$

Substituting h into the first equation, we get: $$l \times w \times 8 = 512$$

Solving for l, we get: $$l = \frac{512}{8 \times w}$$

Substituting l into the second equation, we get: $$\frac{512}{8 \times w \times 4}$$

Simplifying, we get: $$\frac{16}{w}$$

This is the length of the side of the cube, since the cube has equal sides. Therefore, the area of one face of the cube is: $$\left(\frac{16}{w}\right)^2$$

To find the value of w, we can use any of the equations that involve w. For example, using the third equation, we get: $$\frac{w}{2} = \frac{16}{w}$$

Cross-multiplying, we get: $$w^2 = 32$$

Taking the positive square root, we get: $$w = \sqrt{32}$$

Therefore, the area of one face of the cube is: $$\left(\frac{16}{\sqrt{32}}\right)^2$$

Simplifying, we get: $$\frac{64}{8}$$

The final answer is: 8 cm²

I hope this helps you with your Olympiad. Good luck!