+0  
 
0
50
1
avatar+10 

A point in space (x,y,z) is randomly selected so that -1<= x <= 1,-1<= y <= 1,-1<= z <= 1. What is the probability that x^2+y^2+z^2<= 1?

 Apr 26, 2020
 #1
avatar+21017 
+1

A sphere of radius 1 is placed inside a cube with side length 2.

What is the probaility that a randomlychosen point is inside the sphere?

 

Volume of the sphere:  V  =  (4/3)·pi·r3    --->     V  =  (4/3)·pi·13​     --->     V  =  (4/3)·pi

 

Volume of the cube:  V  =  s3     --->     V  =  23     --->     V  =  8

 

Probability:  (4/3)·pi / 8

 Apr 26, 2020

15 Online Users

avatar
avatar
avatar