Question

радиус основания конуса относится к образующей ,как 4:5 , а высота конуса равна 6 см. найдите площадь полной поверхности конуса​

Answer 1

Ответ:R²=l²-h²=5²-4²=3², R=3. Sпол=Sбок+Sосн=пиRl+пиR²=пи(3*5+3²)=24пиR

Пошаговое объяснение:

Answer 2

Finding the Surface Area of a Cone

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

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 that the radius of the base of the cone is in a 4:5 ratio to the slant height, and the height of the cone is 6 cm, we can calculate the surface area using the given information.

Calculating the Radius and Slant Height

First, let's calculate the radius and the slant height of the cone.

The radius of the base of the cone can be calculated using the given ratio and the height of the cone: r = (4/5) * h

Substituting the given height (h = 6 cm) into the formula: r = (4/5) * 6 = 4.8 cm

Now, we can calculate the slant height using the Pythagorean theorem: l = √(r^2 + h^2)

Substituting the values: l = √(4.8^2 + 6^2) = √(23.04 + 36) = √59.04 ≈ 7.68 cm

Calculating the Surface Area

Now that we have the radius (r ≈ 4.8 cm) and the slant height (l ≈ 7.68 cm), we can calculate the surface area of the cone using the formula: Surface Area = πr(l + r)

Substitute the values: Surface Area = π * 4.8(7.68 + 4.8) Surface Area ≈ 3.14 * 4.8 * 12.48 Surface Area ≈ 188.16 cm^2

So, the surface area of the cone is approximately 188.16 square centimeters.