Question

В первом цилиндрическом сосуде уровень жидкости достигает 16 см. Эту жидкость перелили во второй цилиндрический сосуд, диаметр основания которого в 2 раза больше диаметра основания первого. На какой высоте будет находиться уровень жидкости во втором сосуде?

Answer 1

Vцил=Sосн*Н
 
V₁=S₁*H₁. V₁=πR₁² *16
V₂=S₂*H₂.  V₂=π(2*R₁)² *H₂

по условию V₁=V₂ - объём воды

π*R₁² *16=π*4*R₁² * H₂. 16=4H₂. Н=4

ответ: высота воды во втором сосуде 4 см

Answer 2

Calculation of the Liquid Level in the Second Cylinder

To determine the height at which the liquid level will be in the second cylinder, we need to consider the relationship between the volumes of the two cylinders.

Let's assume that the height of the liquid in the first cylinder is h1 and the height of the liquid in the second cylinder is h2. We are given that the diameter of the base of the second cylinder is twice the diameter of the base of the first cylinder.

From the formula for the volume of a cylinder, we know that the volume is directly proportional to the square of the radius and the height of the cylinder. Since the diameter is twice the radius, the volume of the second cylinder will be four times the volume of the first cylinder.

Therefore, we can write the following equation:

(Volume of the first cylinder) = (Volume of the second cylinder)

π * r1^2 * h1 = π * r2^2 * h2

Since the diameter of the base of the second cylinder is twice the diameter of the base of the first cylinder, we can write:

(r2)^2 = (2 * r1)^2

Simplifying the equation, we get:

4 * r1^2 = r2^2

Substituting this into the equation for the volumes, we have:

π * r1^2 * h1 = π * (4 * r1^2) * h2

Simplifying further, we get:

h1 = 4 * h2

Therefore, the height of the liquid in the second cylinder will be one-fourth of the height of the liquid in the first cylinder.

Now, given that the liquid level in the first cylinder is 16 cm, we can calculate the height of the liquid level in the second cylinder:

h2 = (1/4) * h1 = (1/4) * 16 cm = 4 cm

Therefore, the liquid level in the second cylinder will be 4 cm.