![](data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 72 71" width="72"></svg>)
What is the probability that the distance between P and each surface area of the cube is greater than 3 / a if we randomly take a point P in the cube ABCD ABCD with edge length a
The solution to this problem is two volume ratios
Make a cube that coincides with the center of gravity of the cube, and its edge length is a / 3
All the points that satisfy the condition are in this cube
So probability: (A / 3) ^ 3 / A ^ 3 = 1 / 27
RELATED INFORMATIONS
- 1. The lower part of a trapezoid is three times the upper part. The upper part is extended by eight centimeters to form a parallelogram with an area of 288 square centimeters. The area of the original trapezoid is calculated
- 2. If △ ABC ∽ a'b'c ', BC; b'c' = 2; 3, the sum of their circumferences is 15 and the difference of their areas is 20, find the respective circumferences and areas of the two triangles
- 3. Arrange 3 ^ - 55,4 ^ - 44,5 ^ - 33 from small to large
- 4. A plan of rectangular foundation is drawn on a 1 / 2000 scale drawing. How many square meters is the actual floor area of this foundation? Please write a formula
- 5. A mathematical problem of linear equation with one variable If you plant 10 saplings per person, there will be 6 saplings left; if you plant 12 saplings per person, there will be 6 saplings missing. How many people plant trees?
- 6. A regular hexagon is divided into eight parts of equal area This is a mathematical modeling problem, can not be measured
- 7. Give examples of using neutralization reaction in life
- 8. Given the parallelepiped abcd-a'b'c'd '. Find the vector AC' + the vector d'b-the vector DC
- 9. Bo is the middle line on the hypotenuse of right triangle ABC, extend Bo to point D, make Bo = do, connect ad CD, prove that quadrilateral ABCD is a rectangle
- 10. Senior high school mathematics compulsory 5 chapter 3 inequality review reference questions answers
- 11. If we know that the sum of the two right sides of a right triangle is equal to 8 and what are the two right sides, what is the maximum area of the right triangle?
- 12. How to prove that a graph is centrosymmetric, congruent or other?
- 13. There are 324 squares on a go board, each with a piece If the result of the game is: Black accounts for half of the total, white accounts for a quarter of the total. Then who wins the game?
- 14. The maximum value of quadratic function y = - x ^ 2-4x + 3 and the equation of symmetry axis are
- 15. As shown in the figure, in square ABCD, e is the point on DC, connect be, make CF ⊥ be at P, intersect ad at F, if AP = ab
- 16. How to measure quadrilateral area in Geometer's Sketchpad? How to select the interior of quadrilateral?
- 17. Let f (x) be any function defined on (- A, a). It is proved that G (x) = f (x) + F (- x) is an even function, H (x) = f (x) - f (- x) is an odd function, and X belongs to (- A, a) Please; ah
- 18. The quadratic function f (x) satisfies f (2 + x) = f (2-x), f (2) = 1, f (0) = 3. If f (x) has a minimum value of 1 and a maximum value of 3 on [0, M], then the value range of M is
- 19. Physical conversion: 1.5.2m = --- m 2.9.8m = DM = --- cm 3.207mm = --- M = --- DM 4.3.8km = --- M
- 20. 0025m=()dm=()cm=()mm