Susan made a block with small cubes of 8 cubic cm volume to make a block ,3 small cubes long, 9 small
cubes wide and 5 small cubes deep. She realizes that she has used more small cubes than she really needed.
She realized that she could have glued a fewer number of cubes together to lock like a block with same
dimensions, if it were made hollow. What is the minimum number of cubes that she needs to make the block?
a) 114 b) 135 c) 21 d) 71

• as the volume of the small cube is 8 cubic cm, the side length of the cube is 8^(1/3) = 2 cm.
  the length of the block is 3 cubes = 6 cm
  its width is 9 cubes = 18 cm
  depth is 5 cubes = 10cm.
  
  the block is a cuboid and it has six faces.
  lets consider the top and the bottom faces first.
  its length is 3 cubes and width 9 cubes. so totally we need 3*9 cubes in each face.
  so the top and bottom requires 54 cubes.
  
  then lets consider two opposite faces with its length and height.
  it is 3 cubes long and 5 cubes tall. so number of cubes required is 3*5. but since already the top and bottom faces covered one cube height each, the total number of cubes required is 3*3.
  so it is 18 cubes considering the two faces.
  
  then lets consider the remaining two opposite faces.
  it is 9 cubes wide and 5 cubes tall. but since we considered the remaining four faces the dimensions get reduced by a unit cube length each. so the number of cubes required is 7*3
  it amounts to 42 cubes in those two faces.
  
  totally 54+42+18= 114 cubes
  
• 8 years agoHelpfull: Yes(4) No(0)
• 3*9*5= 135
  (3-2)*(9-2)*(5-2) = 21
  
  =135-21= 114
• 3 years agoHelpfull: Yes(0) No(0)