Question

В сосуд, имеющий форму конуса налили жидкость до уровня 2/3 высоты. Найдите V конуса, если V жидкости равен 81.

Answer 1

V(жидкости) = 2 / 3 h
81 = 2h/3
h = (81 * 3) / 2 = 121,5 см
V(конуса) = 1 /3 * (81 + 121,5)  * pi =  67,5pi см^3

Answer 2

H1 = 2/3 * h
V = S * h (конус)
V1 = S * h1 (жидкость)
Подставляем вместо h1 -> h
V1 = S * h * 2/3 = V * 2/3
81 = V * 2/3
V = 121.5

Answer 3

Problem Analysis

We are given a vessel in the shape of a cone that is filled with liquid up to 2/3 of its height. We need to find the volume of the cone if the volume of the liquid is 81.

Solution

To solve this problem, we can use the formula for the volume of a cone, which is given by:

V = (1/3) * π * r^2 * h

where V is the volume, π is a mathematical constant approximately equal to 3.14159, r is the radius of the base of the cone, and h is the height of the cone.

In this case, we are given that the volume of the liquid is 81. Let's assume that the height of the cone is h and the radius of the base is r. We are also given that the liquid fills up 2/3 of the height of the cone.

Since the liquid fills up 2/3 of the height, the height of the liquid can be expressed as (2/3) * h. Therefore, the volume of the liquid can be expressed as:

V_liquid = (1/3) * π * r^2 * (2/3) * h

We are given that V_liquid is equal to 81. Therefore, we can write the equation as:

81 = (1/3) * π * r^2 * (2/3) * h

Now, we can solve this equation to find the value of V, the volume of the cone.

Calculation

Let's calculate the volume of the cone using the given information.

From the equation above, we have:

81 = (1/3) * π * r^2 * (2/3) * h

Simplifying the equation, we get:

81 = (2/9) * π * r^2 * h

Multiplying both sides of the equation by 9/2, we get:

(9/2) * 81 = π * r^2 * h

Simplifying further, we have:

364.5 = π * r^2 * h

Now, we need to find the value of V, the volume of the cone. The volume of the cone is given by:

V = (1/3) * π * r^2 * h

Substituting the value of π * r^2 * h from the previous equation, we get:

V = (1/3) * 364.5

Calculating the value, we find:

V ≈ 121.5

Therefore, the volume of the cone is approximately 121.5.

Answer

The volume of the cone is approximately 121.5.