Question

На расстоянии 8 см от центра шара проведено сечение, длина окружности которого равна 12π см. Найдите площадь его поверхности ПОМОГИТЕ ПОЖАЛУЙСТА, НУЖНО С РИСУНКОМ

Answer 1

Если  длина окружности сечения равна $12\pi$  то тогда радиус окружности будет равен  $2\pi\ r=12\pi\\ r=6$ Следовательно радиус самого шара будет по теореме Пифагора равна $R=\sqrt{8^2+6^2}=10$ 
$S=4\pi*R^2=4\pi*10^2=400\pi$

Answer 2

Task: Finding the Surface Area of a Sphere

To find the surface area of a sphere, we need to know the radius of the sphere. However, in the given question, we are provided with the length of a circumference that is formed by a section of the sphere, which is 12π cm. We are also given that the section is made at a distance of 8 cm from the center of the sphere.

To solve this problem, we can use the relationship between the circumference of a circle and its radius. The formula for the circumference of a circle is given by:

C = 2πr

where C is the circumference and r is the radius of the circle.

In this case, we are given the length of the circumference, which is 12π cm. We can set up an equation using this information:

12π = 2πr

To find the radius, we can solve this equation for r:

r = (12π) / (2π) = 6 cm

Now that we have the radius of the sphere, we can calculate its surface area using the formula:

Surface Area = 4πr^2

Substituting the value of r, we get:

Surface Area = 4π(6^2) = 4π(36) = 144π cm^2

Therefore, the surface area of the sphere is 144π cm^2.

Please note that the above solution assumes that the section made at a distance of 8 cm from the center of the sphere is a circular section. If the section is a different shape, the calculation may vary.

I hope this helps! Let me know if you have any further questions.