Find the maximum volume a right circular cone that can fit inside a cuboid of size 10x15x12.

• Since base circle will be in 2-D and so radius will be 5 in 10x12 plane and height will be 15 for the vol to be maximum.
  So max possible vol is
  1/3*π*5*5*15= 125π
  
  Now I'll make some comments, it will be helpful to visualize the situation.
  
  1. why 15/2 will not be r because it will be a circle in 2D and none of the other side is 15 or greater.
  
  2. If you will take r=6 then height can't be 15. Because again in 10x12 plane circle is not possible with r=6. If you will take r=6 then height will be 10. Then ans will be 120π.
• 7 years agoHelpfull: Yes(11) No(0)
• formula is 1/3 pie*r^2*h
  so clearly if r will be max so volume will be max
  so take breadth as a base of cone the radius will be= 15/2 and take width as a hieght
  volume will =1/3*15/2*15/2*12*pie
  ans would be 225pie
• 7 years agoHelpfull: Yes(1) No(10)
• put r=6 and h=15 calculate
  
  volume of cone as = 1/3*r*r*h*pie
  answer would be=180pie
• 7 years agoHelpfull: Yes(0) No(17)