Question

Шар радиус которого равен 30 дм пересечен плоскостью на расстоянии 8 дм от центра.найдите площадь сечения

Answer 1

Квадрат радиуса сечения по теореме Пифагора равен 30^2-8^2=836
Площадь сечения пи на радиус в квадрате 836π=~2625 дм^2

Answer 2

Calculation of the Section Area

To find the area of the section formed by the intersection of a sphere with a plane, we need to know the radius of the sphere and the distance of the plane from the center of the sphere.

In this case, the radius of the sphere is given as 30 dm (decimeters), and the plane intersects the sphere at a distance of 8 dm from the center.

To calculate the area of the section, we can use the formula for the area of a circle, since the section is a circle. The formula for the area of a circle is:

Area = π * r^2

where π is a mathematical constant approximately equal to 3.14159, and r is the radius of the circle.

In this case, the radius of the circle is the same as the radius of the sphere, which is 30 dm. So we can substitute the values into the formula:

Area = π * (30 dm)^2

Now we can calculate the area using the given values.

Calculation:

Area = π * (30 dm)^2

Using the value of π as approximately 3.14159:

Area = 3.14159 * (30 dm)^2

Simplifying the equation:

Area = 3.14159 * 900 dm^2

Calculating the result:

Area ≈ 2827.43339 dm^2

Therefore, the approximate area of the section formed by the intersection of the sphere with the plane is 2827.43339 square decimeters.

Please note that the above calculation assumes that the section formed by the intersection is a perfect circle.