A cut on a solid object divides the object into two parts where the new surfaces thus produced are p — CSAT 2026 Answer & Explanation

2026

A cut on a solid object divides the object into two parts where the new surfaces thus produced are plane. On the other hand, one single cut can be used to cut more than one object at a time. In an experiment, the total number of pieces produced by applying n cuts is denoted by xₙ. The experiment is performed on a solid cube where pieces remain unmoved after each cut. In this experiment, if after the third cut, the pieces are identical, then which of the following is not a possible value for x₄?

Explanation

After three cuts of a solid cube, the maximum pieces obtainable follows the formula $x_n = \frac{n(n+1)(n+2)}{6}$ for three-dimensional objects. Thus, for $n = 3$ , $x_3 = 10$ . The next possible values for $x_4$ must be less than or equal to $\frac{4(4+1)(4+2)}{6} = 20$ while maintaining that they are identical pieces. Since $16$ does not align with the possible maximum counts of identical pieces produced by four cuts, it is not a possible value for $x_4$ .

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