Question

Шар пересечен плоскостью на расстоянии 4 от центра найдите радиус сечения если радиус шара равен 5

Answer 1

Файл смотри)))))))))))))))))))

Answer 2

Finding the Radius of the Intersection of a Sphere and a Plane

To find the radius of the intersection of a sphere and a plane, we need to consider the properties of both the sphere and the plane. Let's break down the problem step by step.

Given: - Radius of the sphere (r) = 5 - Distance of the plane from the center of the sphere (d) = 4

Understanding the Problem

In this scenario, the sphere is intersected by a plane. The intersection forms a circle on the surface of the sphere. We need to find the radius of this circle.

Solution

To find the radius of the intersection circle, we can use the Pythagorean theorem. The distance from the center of the sphere to the intersection circle is the hypotenuse of a right triangle, with the radius of the sphere (r) as one side and the distance of the plane from the center of the sphere (d) as the other side.

Using the Pythagorean theorem, we can calculate the radius of the intersection circle (R) as follows:

R = √(r^2 - d^2)

Substituting the given values, we have:

R = √(5^2 - 4^2) = √(25 - 16) = √9 = 3

Therefore, the radius of the intersection circle is 3.

Conclusion

The radius of the intersection circle formed by a sphere and a plane, given that the radius of the sphere is 5 and the distance of the plane from the center of the sphere is 4, is 3.

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