In the cube abcd-a1b1c1d1 with edge length a, randomly take the point m in the cube. (1) find the probability that the distance between M and surface ABCD is greater than a / 3 (2) Find the probability that the distance between M and face ABCD and face a1b1c1d1 is greater than a / 3

In the cube abcd-a1b1c1d1 with edge length a, randomly take the point m in the cube. (1) find the probability that the distance between M and surface ABCD is greater than a / 3 (2) Find the probability that the distance between M and face ABCD and face a1b1c1d1 is greater than a / 3

Let A2 and A3 be the trisection points on Aa1, namely aa2 = a2a3 = a3a1 = A / 3. Let B2 and B3 be the trisection points on BB1, namely BB2 = b2b3 = b3b1 = A / 3. Let C2 and C3 be the trisection points on CC1, namely CC2 = c2c3 = c3c1 = A / 3. Let D2 and D3 be the trisection points on dd1, namely DD2 = d2d3 = d3d1 = A / 3

In the cube abcd-a1b1c1d1 with edge length a, what is the probability that the distance from any point P to a is less than or equal to a?

Calculate by volume
The volume of a cube with volume a is S1
Then calculate the volume of the sphere with a radius of 1 / 8 S2
S2 / S1 * 100% is

If any point is selected in the cube abcd-a1b1c1d1 with edge length a, the probability that the distance from point P to point a is less than or equal to a is ()
A. 22B. 22πC. 16πD. 16

This problem is a geometric type problem. The trajectory of a point whose distance from point a is equal to a is an eighth sphere, and its volume is: V1 =, 18 × 4 π 3 × A3 = π 6a3. The volume of the region corresponding to the event of "probability of distance between point P and point O greater than 1" is: 18 × 4 π 3 × A3 = π 6a3. Then the probability of distance from point P to point a less than or equal to a is: π 6a3a3 = 16 π

If any point P is selected in the cube abcd-a1b1c1d1 with edge length a, the probability that the distance from point P to point a is less than or equal to a is 0
I don't know why "the trajectory of a point whose distance from point a is equal to a is an eighth sphere"

Probability = (4 / 3 π a ^ 3) × (1 / 8) / A ^ 3 = π / 6
The distance between P and point a is less than or equal to a. the range of P is a sphere, and the center of the sphere is point a. the part of the sphere falling in the cube is only 1 / 8 of the whole sphere
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