7. 125 small but identical cubes are put together to form a large cube. This large cube is now painted on all six faces.
(i) How many of the smaller cubes have no face painted at all.
(a) 27 (b) 64 (c) 8 (d) 36

(ii) How many of the smaller cubes have exactly three faces painted?
(a) 98 (b) 100 (c) 96 (d) 95


(iii) How many of the smaller cubes have atleast one side painted?
(a) 4 (b) 8 (c) 9 (d) 27

• Side of larger cube is cuberoot(125) = 5
  
  i) No face painted ll be in the interior part of the cube
  Interior part ll be a cube of side (5-2) = 3...
  Hence no. of cubes with no face painted ll be 3^3 = 27
  Ans : (a) 27
  
  ii) Cubes with 3 faces painted ll be the vertices of the cube
  There ll be 8 such cubes
  Ans : 8 [Wrong options... 3rd options should come here]
  
  iii) Atleast 1 face painted => greater than or equal to 1
  Cube with 1 face painted + cube with 2 side painted + cube with 3 side painted
  Cube with 1 face painted ll be the outermost layer of larger cube but not on the edges...
  i.e. (5-2)^2 = 9 cubes on 1 side... So totally 6*9 = 54 cubes
  Cube with 2 face painted ll be edges of the larger cube but
  (5-2) = 3... Since a cube has 12 edges, totally 12*3 = 36 cubes
  Cube with 3 sides painted = 8 cubes
  Totally 54+36+8 = 98 cubes
  Ans : 98
  
• 10 years agoHelpfull: Yes(67) No(1)
• 1)
  inner cubes inside outer cube=(5-2)^(5-2)=3^3=27
  
  no of smaller cubes with no face painted=27
  
  2)
  smaller cubes having exactly 3 faces painted=no of corners=8
  
  3)no of smaller cubes having at least 1 face painted=all cubes-not painted cubes
  =125-27
  =98
• 10 years agoHelpfull: Yes(16) No(0)
• (i)The large cube will have sides of length 5 cube(cube root of 125)
  Therefore all the 6 sides of the large cube will have=5x5=25 cubes
  Cubes with atleast one face painted=Outer cubes.
  No of cubes on top side=5x5=25
  No of cubes on bottom side=5x5=25
  No of cubes on left side=5x3=15
  No of cubes on right side=5x3=15
  No of cubes on front side=3x3=9
  No of cubes on back side=3x3=9
  Total no of cubes with atleast one face painted=25+25+15+15+9+9=98
  Therefore no of cubes with no face painted=125-98=27
  
  Answer = option (a)
  
  
  (ii)The cubes with exactly 3 faces painted are the cubes at the 8 corners
  Answer = 8
  (Incorrect options are given)
  
  (iii)Total no of cubes with atleast one face painted=25+25+15+15+9+9=98
  Answer = 8
  (Again,incorrect options are given)
  
  
  By mistake the options of Questions (ii) & (iii) have been swapped
  
• 10 years agoHelpfull: Yes(10) No(3)
• (i)a
  (ii)8
  (iii)98
• 10 years agoHelpfull: Yes(4) No(2)
• 8.... 1 in each corner....
• 10 years agoHelpfull: Yes(0) No(1)
• 7.(i)a
  calculation
  
• 10 years agoHelpfull: Yes(0) No(2)
• please send me the infosys Placement papers. ashokdevagiri21@gmail.com
• 6 years agoHelpfull: Yes(0) No(0)