Tbe dimensions of an open box are 50 cm, 40 cm and 23 cm. Its thickness is 2 cm. If 1 cubic cm of metal used in the box weighs 0.5 gms, find the weight of the box.

• external volume of box is 50*40*23 cm^3
  remember the box is open, so if we consider inner part of box,
  length will be reduced to 46, because each side 2cm thickness we have so 50-4.
  similarly width also reduced to 36 (40-4).
  but coming to height top is open, so height will be reduced only from bottom to 21 (23-2).
  so internal measurements are 46,36,21
  internal volume of box is 46*36*21
  so metal volume is external volume-internal volume
  ie., (50*40*23)-(46*36*21)
  =(2*25*2*20*23)-(2*23*2*18*21)
  =(4*25*20*23)-(4*23*18*21)
  =4*23*(25*20-18*21)
  =4*23*(500-378)
  =4*23*122 cm^3
  
  each cm^3 it's of 1/2 gm weight, so total weight of the box is
  =4*23*122/2=2*23*122=46*122=5612gms...
• 12 years agoHelpfull: Yes(24) No(1)
• if you want it's simply
  volume of metal is external volume of cube-internal volume of cube=(50*40*23)-(46*36*21)=46000-34776
  =11224 cm^3
  weight of the metal=11224 cm^3 * 0.5 gm/cm^3 =5612 gm or 5.612 kg
• 12 years agoHelpfull: Yes(9) No(0)
• External volume of box=(l*b*h)=(50*40*23)=46000cc
  box is 2cm thick and open from top
  hence, new l=(50-2-2)=46cm
  new b=(40-2-2)=36cm
  new h=(23-2) =21cm
  Internal volume of box=(46*36*21)=34776cc
  
  Metal volume of box=46000-34776=11224cc
  
  Given Density of metal=0.5g/cc
  hence, weight of box =(0.5g/cc)*(11224cc)= 5612g = 5.612kg
• 12 years agoHelpfull: Yes(5) No(0)
• metal is used on the outerpart(circumference of box) oly.. so we have to consider the volume of the outer layer of box
  outer volume-inner voluue
  =50*40*23-46*36*21 (21 coz one side of box is open )
  =11224
  11224*0.5=5612 g is ans
  
• 12 years agoHelpfull: Yes(4) No(0)
• external volume of box is 50*40*23 cm^3
  remember the box is open, so if we consider inner part of box,
  length will be reduced to 46, because each side 2cm thickness we have so 50-4.
  similarly width also reduced to 36 (40-4).
  but coming to height top is open, so height will be reduced only from bottom to 21 (23-2).
  so internal measurements are 46,36,21
  internal volume of box is 46*36*21
  so metal volume is external volume-internal volume
  ie., (50*40*23)-(46*36*21)
  =(2*25*2*20*23)-(2*23*2*18*21)
  =(4*25*20*23)-(4*23*18*21)
  =4*23*(25*20-18*21)
  =4*23*(500-378)
  =4*23*122 cm^3
  
  each cm^3 it's of 1/2 gm weight, so total weight of the box is
  =4*23*122/2=2*23*122=46*122=5612gms...
• 12 years agoHelpfull: Yes(4) No(0)
• volume of box (50*40*23)-(46*36*19)=14536
  no of cube required = 14536/1*1*1=14536
  weight of box=14536*0.5=7268 gm= 7.2 kg
• 12 years agoHelpfull: Yes(3) No(4)