Question

A cube is cut parallel to one face by making 5 cuts such that all the resulting pieces are identical. What is the maximum number of identical pieces that can be obtained now by making 10 more cuts in any direction.

Answer 1

5×10=50

(a)^2=(50)^2=100

Answer 2

• Suppose the 5 cuts were made along the x axis.
• For maximum identical pieces we have to make equal cuts along all the 3 axis.
• Since 5 cuts are made already in the x axis, the remaining 10 cuts should made in the y and z axis with 5 cuts each.
• If p,q,r cuts are made along the 3 mutually perpendicular axis,the number of identical pieces formed = (p+1)(q+1)(r+1).
• So here p=q=r=5.
• (5+1)(5+1)(5+1)=216

∴The number of maximum identical pieces possible = 216