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Know the logic for solving questions on painted cubes
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In exams like CAT, where time management plays a major role - identifying the question type by recalling the concept in first few seconds is extremely important. Chaitanya has amazingly segregated the cube based questions into three types. In this lesson, with help of a few examples he explains the third type of questions where cubes are painted and cut, supporting them with a few simple formulas.

Chaitanya K
Graduated from IIM A

Unacademy user
Hello I have a doubt A cube of 7cm*7cm*7cm is kept in the corner of a room & painted in 3 different colours, each face in one colour. The cube is cut into 343 smaller but identical cubes. 1) how many smaller cubes do not have any face painted? 2) how many smaller cubes have exactly one colour on them? 3) how many smaller cubes have atmost 2 faces painted?
A cube is cut in two equal parts along a plane parallel to one of its faces. One piece is then coloured red on the two larger faces and green on the remaining, while the other is coloured green on two smaller adjacent faces and red on the remaining. Each is then cut into 32 cubes of same size and mixed up. Q 1) How many cubes have only one coloured face each ? Q 2) What is the number of cubes with at least one green face each ? Q 3) How many cubes have two red and one green face on each ?
hi, approach to solve this? A cube is painted with blue color on its all six faces.If this cube is cut into 27 small cubes,and each of the 27 small cubes is cut into 64 small cubes, how many of the smallest cubes will have at least one face colored?
Sir could you tell me that P part. You said it is P^3 smaller pieces but what if it is an uneven cube that has no perfect cube root. What would have been the P if in the later example the cubes were cut into 126 pieces?
I have a doubt. The cubes that will be cut and will be along the edges of the bigger cube, their surface will be painted on 4 sides and 2 sides will have to be painted but for surfaces not along the common edges, only 3 surface will be painted black and rest 3 surfaces have to be painted again with black colour. Can you please help me visualising and rectify my doubt? Thanks
Same query, I think 3 faces will be visible since we are making the cuts throughout the length, breadth and height

  2. About Me . MBA from IIMA Electronics and Software Engineer - 2Years Teaching Experience : 3 Years Course Fees: CONTRIBUTE Follow me on Unacademy: Electronics and Communication Engineer httpslunacademy.inuserchaitanyaunacademy

  3. 1) What is the minimum number of cuts needed to make 343 identical pieces of a cube? (a+1 )(b+1 )(c+1 ) = 343 7*7*7 = 343 Minimum cuts = a+b+c = 6+6+6 = 18 2) A dice has side of 5 cm and is painted on all the sides by 20 litres of black ink and is then cut into 216 identical pieces. If all the smaller pieces are also coloured then how much more black ink is required to colour them? Amount of black ink depends on Surface Area of the cube = 6*a*a For 2 1 6 pieces = 6*6*6 So No of cuts = 5+5+5 = 15 Each cut makes 2 new surfaces to be painted by black ink= 2*a*a So When 15 cuts are made then area to be painted is 15*(2*a*a) = 30a*a area to be painted is 15* 6a2 needs 20 litres of ink 30a2 needs 20*5 litres = 100 litres of additional ink is required

  4. Concept A cube is painted on all the sides and is then cut into P3 smaller pieces # Pieces that will have all 3 faces painted = 8 i.e Corners of a cube # Pieces that will have exactly 2 faces painted = 12(P-2) # Pieces that will have exactly 1 face painted = 6(P-2)(P-2) # Pieces that will have NO face painted = (P2)(P-2)(P-2) # Additional pieces required to cover the cube = (P+2) 3-P 3

  5. A cube is painted on all 6 faces and is cut into 125 pieces and is combined together to form a large cube All 3 faces painted = 8 cubes All 3 faces painted 8 cubes From the questi Atleast 2 faces painted = exactly 2 + exactly 3 = 12(P-2) + 8 = 12(5-2) +8-44 Exactly 1 face painted = 6(P-2)(P-2) = 6*3*3 = 54 No face painted = (P-20P-20P-2) = 27 on P= 5