Question

Высота конуса равна 4 см, а радиус основания - 3 см. Найти объем и площадь полной поверхности конуса.

Answer 1

Обьем V = pi *r^2*h = 36pi
Площадь полной поверхности
S = 2pi*3*4 + 2pi*9 = 42pi

Answer 2

Given Information

The height of the cone is 4 cm, and the radius of the base is 3 cm.

Volume of the Cone

To find the volume of the cone, we can use the formula:

Volume = (1/3) * π * r^2 * h

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

Substituting the given values into the formula, we get:

Volume = (1/3) * π * (3 cm)^2 * 4 cm

Calculating the volume, we have:

Volume = (1/3) * 3.14159 * 9 cm^2 * 4 cm

Volume ≈ 37.6991 cm^3.

Therefore, the volume of the cone is approximately 37.6991 cubic centimeters.

Surface Area of the Cone

To find the surface area of the cone, we need to calculate the lateral surface area and the base area separately, and then add them together.

The lateral surface area of a cone can be calculated using the formula:

Lateral Surface Area = π * r * l

where r is the radius of the base and l is the slant height of the cone.

The slant height can be found using the Pythagorean theorem:

l = √(r^2 + h^2)

where r is the radius of the base and h is the height of the cone.

Substituting the given values into the formulas, we have:

l = √((3 cm)^2 + (4 cm)^2)

Calculating the slant height, we get:

l ≈ √(9 cm^2 + 16 cm^2) ≈ √(25 cm^2) ≈ 5 cm.

Now, we can calculate the lateral surface area:

Lateral Surface Area = π * 3 cm * 5 cm

Lateral Surface Area ≈ 47.1239 cm^2.

The base area of the cone can be calculated using the formula:

Base Area = π * r^2

Substituting the given values into the formula, we get:

Base Area = π * (3 cm)^2

Calculating the base area, we have:

Base Area ≈ 28.2743 cm^2.

Finally, we can calculate the total surface area by adding the lateral surface area and the base area:

Total Surface Area = Lateral Surface Area + Base Area

Total Surface Area ≈ 47.1239 cm^2 + 28.2743 cm^2

Total Surface Area ≈ 75.3982 cm^2.

Therefore, the total surface area of the cone is approximately 75.3982 square centimeters.

Summary

- The volume of the cone is approximately 37.6991 cubic centimeters. - The total surface area of the cone is approximately 75.3982 square centimeters.

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