Question

Шар радиуса 5 дм пересечен плоскостью на расстоянии 3 дм от центра. Найдите площадь сечения шара.

Answer 1

Если расстояние от сечения до центра 3 ,то проводим два радиуса как на втором рисунке .По теореме Пифагора найдем радиус сечения а затем и площадь

Answer 2

Calculating the Area of the Sphere's Cross-Section

To find the area of the sphere's cross-section, we can use the formula for the area of a circle, as the cross-section of a sphere is a circle.

The radius of the sphere is given as 5 dm, and it is intersected by a plane at a distance of 3 dm from the center. We can use this information to calculate the radius of the circle, which is the cross-section of the sphere.

The radius of the circle can be calculated using the Pythagorean theorem, where the hypotenuse is the radius of the sphere (5 dm) and the distance from the center to the intersecting plane (3 dm).

Using the Pythagorean theorem: radius of the circle = √(radius of the sphere)^2 - (distance from center to plane)^2

Substituting the given values: radius of the circle = √(5 dm)^2 - (3 dm)^2

Calculating the radius of the circle will give us the information needed to find the area of the cross-section.

Let's calculate the radius of the circle.