What is the volume of biggest cone that can be fit in a cuboid of height 12*10*15?

• ans:- 125pi
• 10 years agoHelpfull: Yes(6) No(8)
• If we take choose the 12*15 face of cuboid for the base of cone then clearly the radius of the right circular is 6 and height is 10.
  Hence volume of the cone is= 1⁄3 πr^2h = 120h
• 10 years agoHelpfull: Yes(3) No(2)
• 3 cases are possible of base
  1.(12,10)=>diameter=10 and height=15 volume=(1/3)*pi*5^2*15=125pi
  2.(10,15)=>""""""""=10 """"""""""=12 volume=(1/3)*pi*5^2*12=100pi
  3.(12,15)=>""""""""=12 """"""""""=10 volume=(1/3)*pi*6^2*10=120pi
  clearly the biggest cone area will be 125pi.
• 10 years agoHelpfull: Yes(3) No(1)
• If can take min(12,10)/2 as radius and height as 15
  
  So ans will be 125π
• 10 years agoHelpfull: Yes(2) No(0)
• 12*15*11.6=2088
• 10 years agoHelpfull: Yes(0) No(0)
• 12*10*15 = L*B*H..
  1) Taking 12/2=6 as radius and cone will be formed in a vertical way. So height=15, volume of cone = 180pi
  
  2) Taking 10/2=5 as radius and now cone will be formed in a horizontal way,So height=12, volume of cone = 100pi.
  
  So case 1 is the biggest cone, So 180pi is the answer.
• 10 years agoHelpfull: Yes(0) No(2)
• three kind of bases are there (10,12) or (12,15) or(10,15);
  thus radius and height can be paired as (5,15) or (6,10) or (5,12)
  by considering all this surface with(10,12) has maximum volume;
  thus,volume=(1/3)*pi*(r^2)*h=125*pi=392.7
• 10 years agoHelpfull: Yes(0) No(0)
• check all cases
  best case is
  r=15/2
  h=12
  so, volume= 1/3*pi*r^2*h= 225 pi
  
• 10 years agoHelpfull: Yes(0) No(1)