Question

What is the smallest number of whole logs (density = 760 kg/m³, radius = 0.088 m, length = 2.82 m) that can be used to build a raft that will carry 7 people, each of whom has a mass of 86.0 kg?

Answer 1

Let the smallest number of logs required is N. And given the volume of each log
   
So, the weight of the N logs is ( this is the weight of the raft )
  
And if we assume that each log is fully submerged in water. Then, the volume of the water displaced by each log is equal to the volume of the log itself. So, the total weight of the water displaced by all the logs is
  
And this is the bouyancy force.
And if there are n people each having mass M, then the total weight of the people is
  
Then the floating condition of the raft is (assuming the safety factor for each log to be 1 )
  


  
  
  

Now for the given values,
   
And so,
  
   

So, the lowest number of logs required