Questions about the ball, how many questions about the ball?

Regular quadrangular prism. 1。The radius of the inscribed circumscribed circle, the radius of the inscribed circle is half of the length d of the side of the regular Sitsubishi column = d 2.

The radius of the circumscribed circle is the square diagonal of the square on the side of the square column.

Half = (d 2) * 2

2。。The spherical cut is a square with a side length equal to the length of the side of the regular Sitsubishi column, and a circle is drawn on the inside and outside.

A circle. 3。The spherical distance is equal to the circumscribed circle radius minus the inscribed circle radius = (d 2) * 2 - d 2

d/2)*(2-1)

Regular hexagonal prism. 1.The radius of the circumscribed circle is the length of the side of the hexagonal prism d, and the radius of the inscribed circle is the distance from the center to the side of the hexagonal prism = d * 3

2。。The spherical section is a square with a side length equal to the length of the side of the regular six pillars, and a circle is drawn on the inside and outside.

A circle. 3.The spherical distance is equal to the radius of the circumscribed circle minus the radius of the inscribed circle = d * 3-d

d*(√3-1)

1Inscribed ball radius = half the length of the bottom (square) side (half of the shortest side).

Radius of the inscribed sphere = half of the diagonal of the regular tetraprism.

3.Spherical distance = spherical angle multiplied by spherical radius.

1) The radius is half the diagonal of the body.

2) 3) You didn't say anything specific....

Categories: Entertainment & Leisure >> brain teasers.

Problem description: There are 10 balls, 9 of which are of the same weight. Only the weight of one ruler is different, how can you use the balance to weigh it three times to determine that it is the ball?

Analysis: Divide the 10 balls into four groups: 3, 3, 3, and 1, and represent the four balls and their weights by A, B, C, and D respectively. Put the two groups A and B on the two disks of the balance and weigh them.

1) If a=b, then both a and b are **, and then they are called b and c. If b=c, it is obvious that the ball in d is defective; If B c, then the defective product is in C and the defective product is lighter than **, and then take out 2 balls in C to weigh, you can draw conclusions. In the case of b c, the conclusion can also be drawn along the lines of b c.

2) If a b, then c and d are both **, and then called b and c, then there is b = c, or b c (b c is impossible, why?) If b=c, then the defective product is in a and the defective product is heavier than **, and then take out 2 balls in a to weigh, you can draw conclusions; As in the case of b c, it can also be concluded before imitation.

3) If a b, similar to a b, the analysis can be concluded.

1.About the ball out of bounds: the most common question, and also the most controversial, but"There is only one truth: "The ball goes out of bounds to form a throw-in, a corner, and a goal kick, but there is only one standard" when the ball as a whole crosses the goal line, end line, and outside the edge of the sideline, whether in the air or on the ground, from the outside of the goal

It must be the whole of the ball, and a trace of it is not out of bounds if it is in bounds.

2.About the goal:

A goal is scored when the ball crosses the goal line in its entirety from the goal post and under the crossbar, and has not previously breached the rules of the game. "This is also often controversial. The overall concept is the same as the above out of bounds, please don't make another mistake 1 2 2 3 3 4....

Luo instigated: There is a trace of the outer edge of the hidden friend line that does not count!

3.On offside: "An attacking player is in an offside position if the ball is closer to the opponent's goal line. Excepts are the following:

a.The player is in his own half.

b.At least two opposing players are closer to the opponent's goal line than that player.

When a player kicks or touches the ball and a player of the same team is in an offside position, the referee believes that the player has committed any of the following acts, and it shall be judged offside

a.is interfering with a match or interfering with an opponent;

b.Attempt to gain advantage from an offside position.

A player shall not be judged offside if:

a.The player was only in an offside position;

b.A player receives a goal kick, corner kick or throw-in directly. ”

Because the four balls are tangent to each other, the two balls at the top are connected vertically to the bottom. Let the distance between these two lines be h, then there is (draw a diagram to understand).

h^2+(1/2)^2+(1/2)^2=1^2=>h=√2/2

Therefore, the total height of the water surface required = 1 + 2 2 = (2 + 2) 2 and therefore the volume of water that needs to be injected ===

Back to the owner: 1. FIFA stipulates that the standard football weight is 410 grams (14 ounces) - 450 grams (16 ounces).

2. Basketball standard men's game ball: weight 600g-650g, standard women's game ball: weight 510g-550g, youth game ball: weight 470g-500g, children's game ball: weight 300g-340g

3. The standard weight of volleyball is 260 grams to 280 grams.

4. The standard weight of softball is grams.

5. The standard weight of handball is: 425 grams - 475 grams for men and 325 grams - 400 grams for women.

6. The standard ball weight of rugby balls is: 410 grams to 460 grams.

Hope it helps the landlord!

The bottom side length of the regular quadrangular pyramid O-ABCD is 2, and the length of the side edge is the root number (3)O, and the distance from the projection on the ABCD to the apex of ABCD is the root 2, and the height of the quadrangular pyramid is 1.

Six of these pyramids can be put together to form a large cube (the bottom of the pyramid is the face of the cube, and the apex is at the center of the cube). ）

o is the center of the sphere, 1 is the radius to make a ball, it is obvious that this ball is the inscribed ball of the large cube, and from the symmetry, it can be seen that the common part of the ball and a quadrangular pyramid is 1/6 of the ball

Volume: 4 3 1 6 = 2 9

1Inscribed ball radius = half the length of the bottom (square) side (half of the shortest side).

Radius of the inscribed sphere = half of the diagonal of the regular tetraprism.

2.？3.Spherical distance = spherical centric angle.

Multiply by the ball radius.

Number of vertices: 4 (same) Number of edges: 6 (equal length) Face: 4 (congruent regular triangle) When the edge length is 1, the height: 6 is divided into two parts: 1:3 in the center.

The two high angles are 2*ASIN (6 32362 49 (radian) or 109°28 16 39428 41664 889This value is related to finding the smallest face in three-dimensional space, and it is also the angle of the obtuse angle of the diamond at the bottom of the honeycomb.

Surface area: 3

Volume: 2 Radius of the outer sphere: 6, the volume of the regular tetrahedron accounts for 2*3 of the volume of the outer sphere Approximately the radius of the inscribed sphere: 6, The volume of the inscribed sphere accounts for the volume of the regular tetrahedron *3 Approximately the angle between the two faces:

2*ASIN (3 94173 4077 (radian) or 70°31 43 60571 58335 1107, which complements the two high angles.

r=2s c is obtained by dividing the area of the triangle from the center of the inscribed circle into three equal areas of height, and in the same way, the volume of the triangular pyramid can also be obtained by dividing the center of the inscribed sphere into four equal volumes: v=(1 3)sr, so we get: r=3v s