Question

В ци­лин­дри­че­ском со­су­де уро­вень жид­ко­сти до­сти­га­ет 32 см. На какой вы­со­те будет на­хо­дить­ся уро­вень жидкости, если её пе­ре­лить во вто­рой ци­лин­дри­че­ский сосуд, диа­метр ос­но­ва­ния ко­то­ро­го в 4 раза боль­ше диа­мет­ра ос­но­ва­ния первого? Ответ вы­ра­зи­те в см.

Answer 1

Т.к. цилиндр 1 меньше цилиндра 2 в 4 раза, а в цилиндре 1 уровень воды достигает 32 см, то
уровень воды 2 = 32/4= 8 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 cylindrical vessel, we need to consider the relationship between the volumes of the two cylinders.

Let's assume that the diameter of the first cylinder is D and the height of the liquid level in the first cylinder is h. The volume of a cylinder can be calculated using the formula:

V = πr^2h

where V is the volume, π is a mathematical constant approximately equal to 3.14159, and r is the radius of the cylinder.

Since the diameter of the second cylinder is four times larger than the diameter of the first cylinder, the radius of the second cylinder will be twice the radius of the first cylinder.

Let's denote the radius of the first cylinder as r1 and the radius of the second cylinder as r2. Therefore, r2 = 2r1.

The volume of the liquid in the first cylinder can be calculated as:

V1 = πr1^2h

The volume of the liquid in the second cylinder can be calculated as:

V2 = πr2^2h2

Since the liquid is transferred from the first cylinder to the second cylinder, the volumes of the two cylinders should be equal:

V1 = V2

Substituting the values of r2 and V1 into the equation, we get:

πr1^2h = π(2r1)^2h2

Simplifying the equation, we have:

r1^2h = 4r1^2h2

Dividing both sides of the equation by r1^2, we get:

h = 4h2

Therefore, the height of the liquid level in the second cylinder (h2) will be one-fourth of the height of the liquid level in the first cylinder (h).

Given that the liquid level in the first cylinder is 32 cm, we can calculate the height of the liquid level in the second cylinder as follows:

h2 = (1/4) * h

h2 = (1/4) * 32 cm

h2 = 8 cm

Therefore, the liquid level in the second cylindrical vessel will be at a height of 8 cm.