Question

Предложите способ определения диаметра небольшого Шарика , если в вашем распоряжении имеется мензурка с водой и неограниченное количество одинаковых шариков.

Answer 1

Налить воды, затем на мензурке замерить, потом закинуть шарик, посмотреть на сколько поднимется вода. Из полученного вычти начальное.

Answer 2

Determining the Diameter of a Small Ball Using a Graduated Cylinder and Water

If you have a graduated cylinder with water and an unlimited supply of identical small balls, you can determine the diameter of the ball using the following method:

1. Fill the graduated cylinder with water to a certain level, making sure to note the initial volume of water in the cylinder. 2. Gently drop one of the small balls into the graduated cylinder, ensuring that it is fully submerged in the water. 3. Observe the change in water level in the graduated cylinder and record the final volume of water. 4. Calculate the difference between the initial and final volumes of water. This difference represents the volume of the small ball that was submerged in the water. 5. Use the formula for the volume of a sphere (V = (4/3) * π * r^3) to calculate the radius (r) of the small ball. 6. Finally, double the radius to obtain the diameter of the small ball.

Example Calculation: Let's say the initial volume of water in the graduated cylinder is 50 mL, and after adding the small ball, the final volume of water is 60 mL. The difference in volume is 10 mL.

Using the formula for the volume of a sphere, we can calculate the radius (r) of the small ball: V = (4/3) * π * r^3 10 mL = (4/3) * π * r^3

Solving for r: r^3 = (10 mL * 3) / (4 * π) r^3 ≈ 7.55 mL / π r ≈ (7.55 mL / π)^(1/3)

Finally, we double the radius to obtain the diameter of the small ball: diameter ≈ 2 * r

Please note that the accuracy of this method depends on the precision of the measurements and the assumption that the small balls are perfectly spherical.

I hope this helps! Let me know if you have any further questions.