V=(4/3)πr^3？

Analysis: three quarters times pi times the radius of the cube.

Sphere:

"A ball with the same length in space."

Definition:

(1) The set of points whose distance from a fixed point in the distance space is equal to or less than a fixed length is called a sphere, which is called a sphere for short. (defined from the perspective of set)

(2) Taking the straight line with the diameter of the semicircle as the rotation axis, the rotating body formed by one rotation of the semicircle surface is called a solid ball, which is called a ball for short. (defined from the angle of rotation)

(3) Taking the straight line where the diameter of the circle is located as the rotation axis, the rotating body formed by the rotation of the circular surface by 180 degrees is called a solid ball, which is called a ball for short. (defined from the angle of rotation)

(4) A point set whose distance from a fixed point in space is equal to a fixed length is called a sphere. This fixed point is called the center of the ball, and the fixed length is called the radius of the ball.

Extended data:

First, the basic idea and method of calculating the volume of a sphere:

First, intercept the ball with the plane where the center of the ball is located, and divide the ball into two hemispheres of equal size with the cross section, and the cross section ⊙ is called the bottom surface of the obtained hemisphere.

Step 1: Subparagraph

Cut the hemisphere into layers with a set of planes parallel to the bottom surface.

(2) Step 2: Find approximate sum.

Each layer is an approximately cylindrical "small disk". We use the volume of a small cylinder to approximate the volume of a "small disk", and their sum is the approximate volume of a hemisphere.

(3) Step 3: Convert approximate sum into exact sum.

When it increases infinitely, the approximate volume of the hemisphere tends to the exact volume.

Second, the mathematical language expression:

There is a circle x 2+y 2 = r 2. Let the circle rotate around the X axis on the xoy coordinate axis to get a sphere.

The infinitesimal size of a sphere is dv = π [√ (r 2-x 2)] 2dx.

∫ dv = ∫ π [√ (r 2-x 2)] 2dx integration interval is [-r, r].

Get the following results

4/3πr^3？

References:

Baidu Encyclopedia-Ball (Stereograph)?