Question

Имеются два сосуда емкостью 800см в кубе и 700см в кубе.нальем воду из водопроводного крана.переливая воду из одного сосуда в другой, как можно оставить 300см в кубе воды в сосуде с большей емкостью?

Answer 1

Отвечал уже.
1) Налить полный сосуд 800 куб.см.
2) Аккуратно его наклонить, чтобы вылилась ровно половина.
Например, если сосуд в форме параллелепипеда или цилиндра, то наклонять нужно до тех пор, пока не появится краешек дна.
В сосуде 800 куб. см. осталось 400. Это показано на рисунке.
3) Налить полный сосуд 700 куб.см.
4) Перелить из сосуда 700 в сосуд 800 до полного.
Теперь в сосуде 800 будет 800, а в сосуде 700 будет 300.
5) Вылить 800 и перелить 300 в него.
Всё!

Answer 2

Solving for the Amount of Water in Each Vessel

To solve this problem, we can use a method called the "water pouring problem" or "jug problem." This problem involves transferring water between two containers to achieve a specific amount of water in one of the containers.

Let's denote the capacities of the two vessels as V1 = 800 cm³ and V2 = 700 cm³. We want to find a way to leave 300 cm³ of water in the vessel with the larger capacity after transferring water between the two vessels.

Solution Steps

1. Initial State: Both vessels are empty. 2. Fill V1: Fill vessel V1 (800 cm³) with water from the tap. 3. Transfer to V2: Pour water from V1 to V2 until V1 is empty or V2 is full. 4. Empty V2: If V2 is full, empty it. 5. Transfer from V1 to V2: Pour the remaining water from V1 to V2 until V1 is empty or V2 is full. 6. Fill V1 Again: If V2 is full, fill V1 again and continue pouring water into V2 until V1 is empty or V2 has 300 cm³ of water.

This process will leave 300 cm³ of water in the vessel with the larger capacity.

Mathematical Approach

The solution to this problem involves finding the greatest common divisor (GCD) of the two vessel capacities. The GCD represents the maximum amount of water that can be measured using the vessels.

The GCD of 800 and 700 is 100. This means that it is possible to measure water in increments of 100 cm³ using these vessels.

By following the steps outlined above, it is possible to leave 300 cm³ of water in the vessel with the larger capacity.

I hope this explanation helps! If you have any further questions or need additional clarification, feel free to ask.