Question

Диаметр шара равен m. Через конец диаметра проведена плоскость под углом 45 градусов к нему. Найдите длину линии сечения сферы этой плоскостью.

Answer 1

Это будет гипотенуза прямоугольного треугольника с катетами m/2.
√2(m/2)²=(m/2)·√2

Answer 2

Calculation of the Length of the Intersection Line

To find the length of the intersection line between a sphere and a plane that is inclined at a 45-degree angle to the diameter of the sphere, we can use the following steps:

1. Determine the radius of the sphere: Since the diameter of the sphere is given as m, the radius will be half of that, which is m/2.

2. Calculate the length of the intersection line: The length of the intersection line can be found by multiplying the radius of the sphere by the square root of 2. This is because the intersection line forms a right-angled triangle with the diameter of the sphere, and the angle between the diameter and the intersection line is 45 degrees. The length of the intersection line can be calculated using the formula:

Length of Intersection Line = Radius of Sphere * √2

Substituting the value of the radius, we get:

Length of Intersection Line = (m/2) * √2

Therefore, the length of the intersection line is (m/2) * √2.

Please note that the search results did not provide a direct answer to this specific question. However, the calculation provided above is based on the mathematical relationship between the diameter of a sphere, the angle of inclination of the plane, and the length of the intersection line.