What is the maximum volume of Right Circular cone which can be cut from solid cuboid having dimension 12*10*15

• 
  3 cases possible
  r= min(12,10)/2 = 5 , h = 15 , V = (1/3)*pi*5^2*15 = 125pi
  r= min(12,15)/2 = 6 , h = 10 , V = (1/3)*pi*6^2*10 = 120pi
  r= min(10,15)/2 = 5 , h = 12 , V = (1/3)*pi*5^2*12 = 100pi
  
  maximum volume = 125pi
• 10 years agoHelpfull: Yes(50) No(7)
• Sorry, I went wrong in calculations.. logic is same anyway..
• 10 years agoHelpfull: Yes(4) No(1)
• By calculating the area of the cone one by one for all three bases we could find the greatest among them. Area of a right circular cone = 1/3*pie*r^2*h. Here r^2h has to be the greatest.
  
  Now, inside a rectangle, the maximum radius that a circle can have will be (smaller_side of the rect.)/2.
  The three rectangles for the base of the cone could be (12, 10), (10, 15), and (15, 12).
  We get r^2h as 5^2*12, 5^2*15, and 6^2*15 => 300, 375, and 540.
  Hence we find the greatest r^2h to be 540.
  So, the greatest volume a right circular cone can have is 1/3*pie*r^2*h = 270pie.
• 10 years agoHelpfull: Yes(2) No(10)
• pls explain why to select radius by taking mean of two sides ...??
  
• 10 years agoHelpfull: Yes(2) No(1)
• why radius is taken minimum of two when we want volume to be maximum
• 10 years agoHelpfull: Yes(0) No(0)
• U cant take maximum of radius as u wont be able to create circular base by taking longer side
• 10 years agoHelpfull: Yes(0) No(0)