If each vertex of a regular octahedron with a surface area of 23 is on the same sphere, the volume of the sphere is___ .

If each vertex of a regular octahedron with a surface area of 23 is on the same sphere, the volume of the sphere is___ .

Since each vertex of a regular octahedron with a surface area of 23 is on the same sphere, the area of each side triangle is 34 and it is an equilateral triangle. If its side length is a, then it has 12 × a × a × sin60 ° = 34, and the solution is a = 1. Therefore, the diagonal length of the square composed of four points is 2, and the radius of the ball is 22, so the volume of the ball is 43 & nbsp; × π× (22) 3 = 23 π, so the answer is 23 π
175 exercises on four mixed operations of mathematics scores in Volume 1 of grade 6
It's all simple operations. Don't repeat them
The relationship between linear velocity and angular velocity at any time in circular motion
It's not a uniform circular motion
v=wr
Infinitesimal thought: you divide the circular motion into many parts, one by one, of linear motion, each part is △ L in length, with time △ t △ L = V △ t = α R
At the same time, divide by △ t to get v = α / △ t r = w R
The above idea is not limited to uniform circular motion, but also applicable to variable speed circular motion and irregular curve motion. If it is applied to curve motion, R is the radius of curvature
What is the volume of a regular octahedron whose surface area is a if its vertices are on the same sphere
A regular octahedron has a square surface, so the edge length of the regular octahedron is a / 2, which is the diameter of the ball
The formula of sphere volume is 4 / 3 π R ＾ 3 (R is the radius)
Note: This is to cut the largest ball in the octagon
Sixth grade mathematics
() 3 / 5-2 / 9 × 9 / 10 = 2 / 5
3 / 4 × [(29-700 / 7) × 9 / 7] = 3 / 8
A road repair team built a railway, 28 kilometers in the first day, 5 / 8 less than 7 kilometers in the second day, and 4 / 5 in two days. How many kilometers is the total length of the railway?
[seek explanation]
If the total length is a kilometer, then 2
28+5/8a-7=4/5a
The solution is a = 120
On the angular velocity of circular motion
Does the linear velocity of uniform circular motion change? Is the concept a mess
As shown in the figure: place a small slider at a certain distance from the center of the circle on the horizontal disc that rotates at a constant speed. The slider can just follow the circular motion of the disc at a constant speed without relative sliding. When changing the following conditions, the slider can still keep relatively static with the disc
A. Increase the angular velocity of the disk. B. increase the distance between the slider and the rotating shaft. C. increase the mass of the slider. M.D. the slider can not be stationary relative to the disk under any condition
If f = MV2 / R is used, then r increases and centripetal force decreases. But if mrw2 is used, then r increases and centripetal force increases. That is not contradictory
C. Increase the mass of the slider m, the linear velocity of the uniform circular motion is the same: put a small slider on the horizontal disc at a certain distance from the center of the circle, the slider can just follow the disc to do uniform circular motion, which indicates that the static friction provides centripetal force UMG = MV2 / R, the mass will be about a, and increase the angular velocity of the disc
Friction = centripetal force, mrw2 = UMG, M can be eliminated, so changing m is relatively static
It depends on whether the centripetal force is the same or not
V = WR, the centripetal force is constant
It depends on m. There are two variables in the formula, m and R. it is not enough to determine only one, but the speed will not change
If each vertex of a regular octahedron with a surface area of 2 and a radical of 3 is on the same sphere, the volume of the sphere is?
How do you know that an octahedron is an equilateral triangle with a side length of each face, a = 1 for the ball, and why is the diameter of the ball root 2?
A regular octahedron can be regarded as a geometry formed by bonding the bottom of a square with two regular quadrangular pyramids of equal length
So all its sides are regular triangles with equal sides
The diameter of its circumscribed sphere is any two opposite vertex connecting segments
In fact, it is the diagonal of the square at the bottom of the original pyramid
If the edge length a = 1, then the diagonal of the square is √ 2, which is the diameter of the circumscribed ball!
For the detailed concept of regular octahedron, see resources!
Mathematics problems of primary school students
A barrel of oil weighs 15 kg. If you pour out 5 / 4 of it, it can fill three bottles. How many kg of oil can each bottle hold?
After the technological innovation, the cost of a certain electronic component has been reduced by 20 / 3 and 10 / 3 yuan. What is the cost of this electronic component? What is the current cost?
15 × 4 / 5 △ 3 = 4 kg 3 / 10 △ 3 / 20 = 2 yuan 2 × (1-3 / 20) = 17 / 10 yuan
Relationship between instantaneous velocity and velocity
Speed is the abbreviation of instantaneous speed, which refers to the size of instantaneous speed. The following emphasis: speed is the size of instantaneous speed, but the average speed is not the size of average speed. Average speed = displacement / time. Average speed = distance / time. Generally, the size of displacement and distance are not equal, so the size of average speed is not equal
Velocity is only a quantity of velocity, and instantaneous velocity includes velocity and direction
Speed = distance / time
Velocity = displacement / time
Instantaneous speed: the size of instantaneous speed, also referred to as speed.
The speed of an object at a certain moment in the process of motion is called instantaneous speed, which has no direction. Instantaneous velocity only represents the magnitude of instantaneous velocity, not the direction of instantaneous velocity.
Speed refers to the magnitude of instantaneous speed
If each vertex of a regular octahedron with a surface area of 23 is on the same sphere, the volume of the sphere is___ .
Since each vertex of a regular octahedron with a surface area of 23 is on the same sphere, the area of each side triangle is 34 and it is an equilateral triangle. If its side length is a, then it has 12 × a × a × sin60 ° = 34, and the solution is a = 1. Therefore, the diagonal length of the square composed of four points is 2, and the radius of the ball is 22, so the volume of the ball is 43 & nbsp; × π× (22) 3 = 23 π, so the answer is 23 π