Question

Площадь боковой поверхности конуса равна 540п радиус, основания 18 см. Найти высоту и объем конуса

Answer 1

Вот решение это данной задачи

Answer 2

Calculation of Cone Height and Volume

To find the height and volume of a cone, we need to use the given information about the cone's lateral surface area and the radius of its base.

The formula for the lateral surface area of a cone is given by:

Lateral Surface Area = π * r * l

Where: - π is the mathematical constant pi (approximately 3.14159) - r is the radius of the base of the cone - l is the slant height of the cone

In this case, the lateral surface area is given as 540π and the radius is given as 18 cm.

Let's calculate the slant height first.

Lateral Surface Area = π * r * l 540π = π * 18 * l

Simplifying the equation, we get:

540 = 18 * l l = 540 / 18 l = 30 cm

Now that we have the slant height, we can use it to find the height of the cone using the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (in this case, the slant height) is equal to the sum of the squares of the other two sides (in this case, the height and the radius).

l^2 = h^2 + r^2

Substituting the values we have:

30^2 = h^2 + 18^2 900 = h^2 + 324 h^2 = 900 - 324 h^2 = 576 h = √576 h = 24 cm

So, the height of the cone is 24 cm.

Now, let's calculate the volume of the cone.

The formula for the volume of a cone is given by:

Volume = (1/3) * π * r^2 * h

Substituting the values we have:

Volume = (1/3) * π * 18^2 * 24 Volume = (1/3) * π * 324 * 24 Volume = (1/3) * π * 7776 Volume = 2592π cm^3

Therefore, the volume of the cone is 2592π cm^3.

Please note that the values of the slant height, height, and volume are approximate due to the use of an approximate value for pi (π).

Let me know if there's anything else I can help you with!