As shown in the figure, the left and right are two geometric bodies sandwiched between two parallel planes (the left figure is a hemisphere with a radius of R, and the right figure is a cylinder with a part cut off in the middle, where the bottom radius of the cylinder is R and the height is R, and the cut-off part is a cone with a bottom radius of R and a height of R).
If any plane parallel to these two parallel planes is used to cut these two geometric bodies, the cross section of the left picture is a circle, and the cross section of the right picture is a circle.
The middle part of the figure is the front view of these two geometric figures.
So s circle =?
(H stands for section height) S-ring =? (Zheng Yini = Ji =H)
So s-ring =S-ring.
According to the principle of ancestral pestle, we can get: v hemisphere =?
V ball =
Extended data:
Cut a ball with a plane, the cross section is round. The cross section of the ball has the following characteristics:
1. The straight line connecting the center of the sphere and the center of the section is perpendicular to the section.
2. The distance d from the center of the sphere to the cross section has the following relations with the radius r of the center of the sphere and the radius r of the cross section: r? =R？ -Dee?
A circle whose sphere is cut by a plane passing through the center of the sphere is called a big circle, and a circle cut by a section not passing through the center of the sphere is called a small circle.
On the sphere, the length of the shortest connecting line between two points is the length of the bad arc between these two points through the great circle of these two points. We call this arc length the spherical distance between two points.
The formula for calculating the surface area of a ball with radius r is:
The diagonal of the inscribed cube of the ball is the diameter of the ball.
Standard equation of spherical surface:.
(The center of the represented sphere is (a, b, c) and the radius is R)
References:
Baidu encyclopedia-ball