Question

Радіус основи конуса дорівнює 6 см, а його висота - 8 см. Знайти площу повної поверхні конуса .

Answer 1

Sполн. пов=πRl+πR², где l - образующая конуса
рассмотрим треугольник, в котором высота конуса-катет, радиус основания-катет, угол между высотой и радиусом=90°, образующая-гипотенуза.
по т. Пифагора: l²=R²+H², l=√(8²+6²), l=10 см.
Sполн. пов=π*6*10+π*6²=π*(60+36)=π*96
ответ: S=96π см²

Answer 2

Calculation of the Surface Area of a Cone

To find the surface area of a cone, we need to know the radius of the base and the height of the cone. In this case, the radius of the base is given as 6 cm and the height is given as 8 cm.

The formula for the surface area of a cone is:

Surface Area = π * r * (r + l)

Where: - π is a mathematical constant approximately equal to 3.14159 - r is the radius of the base of the cone - l is the slant height of the cone

To calculate the slant height, we can use the Pythagorean theorem:

l = √(r^2 + h^2)

Where: - h is the height of the cone

Let's calculate the surface area of the cone using the given values:

1. Calculate the slant height: - l = √(6^2 + 8^2) = √(36 + 64) = √100 = 10 cm

2. Calculate the surface area: - Surface Area = π * 6 * (6 + 10) = 16π cm^2

Therefore, the surface area of the cone is 16π cm^2.