What is the number of pieces into which a cube can be cut by 5 cuts in one direction and seven cuts in another direction?

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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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