A sqaure of side 30 cm is given.Four sqaures of equal dimensions are cut from the corners of the sqaure and the corners are folded to make a box.Find the maximum volume of the box ?

• Let the side of four equal squares= x cm.
  
  when we cut the square of x cm from the corners of the square of 30 cm and corners are folded, then the final dimension of the figure is cuboid (i.e. open box).
  
  where,
  l=30-2*x
  b=30-2*x
  and h=x
  
  now,
  volume of cuboid,V=lbh= (30-2*x)*(30-2*x) * x = 4*x^3-120*x^2+900
  
  take dV/dx= 12*x^2-240*x+900
  
  for maximum or minimum condition
  dV/dx=0
  
  so, 12*x^2-240*x-900 = 0
  solving this we get
  x=5 or x=15
  
  since, we have to find the maximum volume of the box, so we take minimum square dimension.
  that is, x=5cm
  
  now, the maximum volume of the box is given by
  
  V=(30-2x)*(30-2x)*x = 20*20*5= 2000 cm^3
  
  
• 10 years agoHelpfull: Yes(8) No(0)
• given side of square=30 cm
  given to form cube
  to form cube we must cut the corners of side 7.5 cm
  so the side of the cube is 15 cm
  volume of the cube=(15)^3=3375 cm^3
  
• 10 years agoHelpfull: Yes(1) No(1)
• i think--ans=13500(cm)3
  Four sqaures of equal dimensions will be of 15cm ,so if put i into matchbox max. vol. will be=15cm*15cm*60cm=13500cm3
• 10 years agoHelpfull: Yes(0) No(1)
• ans is 1000cm3...... as 4 squares of 15 cm sides are there....we can make 6 sides of cube with 10 cm each....therefore volume=10^3=1000cm3
• 10 years agoHelpfull: Yes(0) No(1)