Question

Find the least number of cuts required which can cut a cube into 60 identical pieces?

• A. $9$
• B. $12$
• C. $15$
• D. $5$

Answer 1

The correct option is A $9$

We need to cut a ute to $60$ identical pieces

If we cut oru it become $2$ identical pieces.

If we cut twice on same face it becomes $3$ identical pieces.

If we cute once on one face and another on other face it becomes $4$ identical pieces.

$\therefore$ general formula $\Rightarrow$ number of identical pieces$=(l+1)(m+1)(n+1)$

$(n,m,l)=$ no. of cut on each face

Given:- $(l+1)(m+1)(n+1)=60$

$(l+1)(m+1)(n+1)=3\times 4\times 5$

$\Rightarrow (l+1)=3,m+1=4,n+1=5$

$\Rightarrow l=2,m=3,n=4$

$\therefore$ total no. of cuts $=l+m+n=3+4+2$

$=9$

$\therefore$ minimum $9$ cuts have to be made to get $60$ identical pieces.