How many pieces will you get if you make 4 cuts along the length and 4 cuts along the breadth of a solid cube?

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The following questions are based on the information given below:

  1. A cuboid shaped wooden block has 6 cm length, 4 cm breadth and 1 cm height.
  2. Two faces measuring 4 cm x 1 cm are coloured in black.
  3. Two faces measuring 6 cm x 1 cm are coloured in red.
  4. Two faces measuring 6 cm x 4 cm are coloured in green.
  5. The block is divided into 6 equal cubes of side 1 cm (from 6 cm side), 4 equal cubes of side 1 cm(from 4 cm side).

1. 

How many cubes having red, green and black colours on at least one side of the cube will be formed ?

Answer: Option D

Explanation:

How many pieces will you get if you make 4 cuts along the length and 4 cuts along the breadth of a solid cube?

Such cubes are related to the corners of the cuboid. Since the number of corners of the cuboid is 4.

Hence, the number of such small cubes is 4.

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How many pieces will you get if you make 4 cuts along the length and 4 cuts along the breadth of a solid cube?

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100 Questions 80 Marks 90 Mins

Given: 

A cube that has been applied 13 cuts. 

Concept:

By cutting the cube for the first time, it will be divided into 2 parts. 

By cutting the cube along the perpendicular, it will be divided into 4 parts. 

Again, by cutting the cube along the perpendicular, it will be divided into 8 parts.

⇒ With 3 cuts, there will be a total of 8 cubes.

⇒ It can be concluded that 'n' cuts made along one plane will have 'n + 1' pieces.

Calculation:

To obtain equal pieces, cuts must be made parallel to 3 planes. 

Let's assume, a, b, and c cut made along three planes such that there will be (a + 1)(b + 1)(c + 1) = m pieces & a + b + c = 13. 

⇒ Several combinations can be made but 'm' will be maximum in (4, 4, 5) cuts.

∴ The required number of pieces = m = (4 + 1)(4 + 1)(5 + 1) 

⇒ 5 × 5 × 6 

⇒ 150 

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