A large cube is dipped into a tub filled with colour. When the cube is taken out it was observed that all its sides are painted. This large cube is now cut into 125 small but identical cubes.
with no face painted

• n=5 no painted cubes= (n-2)^3 =27
• 10 years agoHelpfull: Yes(9) No(0)
• Imagine one face and its opposite face. We can count all the painted cubes on each of these faces without risking double counting: 5 x 5 = 25 painted cubes on each face. 2 x 25 = 50 painted cubes in total.
  
  Now picture another two opposite faces. Whichever pair you choose you will have already counted two of the edges on each face. Instead of counting 5*5 painted cubes on each face, you count 5 x 3 = 15, and 2 x 15 = 30 in total.
  
  Now the final pair of faces. All the edges have been counted already so you have 3 x 3 = 9 uncounted painted cubes on each face. 2 x 9 = 18.
  
  so total painted cube is 50+30+18=98
  and unpainted is 125-98=27
• 10 years agoHelpfull: Yes(6) No(0)
• ans 27
  refer cubes problems on The Pearson Complete Guide For The Cat - Sinha Nishit K - Google Books
• 10 years agoHelpfull: Yes(5) No(0)
• A^3= 125a^3 i.e A=5a
  area painted=6*A^2=150a^2
  total area of 125 cubes=750a^2
  unpainted area=600a^2
  area of 1 face=a^2
  so,600 faces not painted
• 10 years agoHelpfull: Yes(4) No(4)
• 150
  25*6=150
• 10 years agoHelpfull: Yes(1) No(1)
• no. of cubes with no face painted=27
• 10 years agoHelpfull: Yes(1) No(0)
• cn anyone plz post the formulas used in these type of qstions...??
• 10 years agoHelpfull: Yes(1) No(0)
• *Aman Sharma,can u pl explain the formula??then it will very helpful for this type of sums..
• 10 years agoHelpfull: Yes(0) No(0)
• no face painted =(125*6)-125
  =525
• 10 years agoHelpfull: Yes(0) No(1)
• ans : 252 sides
  as there are 125 cubes
  out of which 45 are in center having total faces 270
  out of which 18 are colored
  
• 10 years agoHelpfull: Yes(0) No(2)
• 125=5*5*5
  so,no of cubes with no face painted=
  no of cubes inside
  =(5-1)*(5-1)*(5-1)
  =4*4*4=64 ans
• 10 years agoHelpfull: Yes(0) No(0)
• No. Of zero face color= 27
  So no. Of face not color= 27*6= 162
  No. Of 1 face color cube= 54
  So no. Of face not color here= 54*5= 270
  No. Of 2 face color cube= 36
  So. No. Of face not color= 36*4= 144
  No. Of 3 face color cube= 8
  So. No. Of face not color = 8*3= 24
  So. Total face not color = 162+270+144+24= 600
• 10 years agoHelpfull: Yes(0) No(0)
• ans: 250/40 = 6.25
• 10 years agoHelpfull: Yes(0) No(1)
• When the painted cube is cute into 125 small equal cubes, we have:
  A 3 faces painted cube on every corner
  ⇒
  Number of cubes with 3 face painted
  =
  1
  ×
  8
  =
  8
  Three 2-faces painted cube on every edge
  ⇒
  Number of cubes with 2 face painted
  =
  3
  ×
  12
  =
  36
  Nine single face painted cube on side
  ⇒
  Number of cubes with 1 face painted
  =
  9
  ×
  6
  =
  54
  
  ∴
  Number of cubes with no face painted
  =
  125
  −
  8
  −
  36
  −
  54
  =
  27
• 5 Months agoHelpfull: Yes(0) No(0)