Question

шар радиускоторого равен 25дм . пересечен плоскостью на расстоянии 5дм . найдите площадь сечения

Answer 1

Сечение будет кругом, КВАДРАТ радиуса которого равен 25^2-5^2 = 200;

А искомая площадь равна 200*pi, само собой.

Answer 2

Finding the Area of the Section

To find the area of the section of a sphere with a radius of 25 dm, intersected by a plane at a distance of 5 dm, we can use the formula for the area of a circle segment.

The formula for the area of a circle segment is given by:

A = r^2 * (θ - sin(θ)) / 2

Where: - A is the area of the segment - r is the radius of the sphere - θ is the central angle of the segment in radians

Calculating the Central Angle

To calculate the central angle (θ), we can use the following formula:

θ = 2 * arccos((r - h) / r)

Where: - h is the distance from the center of the sphere to the plane

Substituting Values and Calculating

Substituting the given values: - r = 25 dm (radius of the sphere) - h = 5 dm (distance from the center of the sphere to the plane)

We can calculate the central angle (θ) using the formula above and then use it to find the area of the section using the area formula.

Conclusion

By applying the formulas for the area of a circle segment and the central angle, we can find the area of the section of the sphere intersected by the plane at a distance of 5 dm.