Question

Высота конуса 9 см , а объём 6 по см ^3 , найти площадь полной поверхности конуса Прошу помогите пожалуйста

Answer 1

Ответ:

π($\sqrt{166}$ + 2)см

Объяснение:

на фото решение

Answer 2

Calculating the Total Surface Area of a Cone

To find the total surface area of a cone, we can use the formula:

Total Surface Area = πr(l + r)

Where: - r is the radius of the base of the cone - l is the slant height of the cone

Given: - Height of the cone, h = 9 cm - Volume of the cone, V = 6 cm^3

Finding the Radius and Slant Height of the Cone

First, let's find the radius and slant height of the cone using the given information.

The formula for the volume of a cone is: V = (1/3)πr^2h

We are given that the volume, V = 6 cm^3, and the height, h = 9 cm. Using these values, we can solve for the radius, r.

Let's calculate the radius of the cone: 6 = (1/3)πr^2 * 9

Solving for r: r^2 = (6 * 3) / (π * 9) r^2 = 2 / π r = √(2 / π)

Now, we need to find the slant height, l. The slant height can be found using the formula: l = √(r^2 + h^2)

Let's calculate the slant height of the cone using the obtained value of r.

Calculating the Total Surface Area

Now that we have the radius and slant height, we can use the formula to find the total surface area of the cone.

Total Surface Area = πr(l + r)

Let's substitute the values of r and l into the formula to find the total surface area of the cone.