Describe the cross sections formed as the plane intersects the interior of the sphere but moves away from the center
any plane intersection with a sphere is a circle.
Part 2 out of 2
Describe the cross sections formed as the plane intersects the interior of the sphere but moves away from the center.
The cross sections will be circles, but their radii will
increase
as the plane moves away from the sphere's center.
As the plane intersects the interior of the sphere and moves away from the center, the resulting cross sections formed can be classified into three types based on their shapes:
1. Circle: When the plane intersects the sphere at a right angle from the center, the cross section formed is a circle. The size of the circle depends on the distance of the plane from the center of the sphere. As the plane moves farther away from the center, the diameter of the circle increases.
2. Ellipse: When the plane intersects the sphere obliquely, the resulting cross section is an ellipse. The shape of the ellipse is determined by the angle at which the plane intersects the sphere and the orientation of the plane. The major and minor axes of the ellipse represent the longest and shortest distances across the cross section, respectively.
3. Point: When the plane is tangent to the sphere, the resulting cross section is just a single point. This occurs when the plane is parallel to the tangent plane of the sphere at a single point.
It's worth noting that as the plane moves further away from the center, the cross sections formed become larger and their shapes begin to resemble more elongated ellipses.
As the plane intersects the interior of the sphere and moves away from the center, the resulting cross sections change in shape.
Initially, when the plane is very close to the center of the sphere, the cross section formed is a small, nearly circular shape. As the plane continues to move outward, the cross sections gradually increase in size. These cross sections are still circular but become larger in diameter.
Once the plane is equidistant from the center of the sphere, the cross section takes on its maximum size, which is the diameter of the sphere. At this point, the cross section is a perfect circle.
As the plane continues to move away from the center of the sphere, the cross sections gradually decrease in size, becoming smaller circles until they ultimately shrink to a single point when the plane is infinitely far away from the center of the sphere.
In summary, the cross sections formed as the plane intersects the interior of the sphere and moves away from the center start as small circles, increase in size to form larger circles, reach maximum size as a circle equal in diameter to the sphere, then decrease in size until they become infinitely small circles and eventually collapse to a single point.