Page 244 - Services Selection Board (SSB) Interviews

Chapter
Chapter
18 Cubes

Section Level No. of Questions
Concept Applicator Very Easy 20

Concept Builder Easy 50

INTRODUCTION

The questions based on cubes, test the ability of the students to visualize and deal with the multidimensional problems/
situations.
If you consider all the exams together, CAT/XAT/IIFT/FMS/JMET/CET/SNAP/MAT you will get at-least one question
from this topic.
In a cube:
Number of vertices V = 8
Number of Faces F = 6
Number of Edges E = 12
We know the Euler’s formula F + V = E + 2
If we make a cut in one plane then we divide the cube in two parts (as shown in fig 1) , if we make 2 cuts in same plane
then we will get 2 + 1 = 3 pieces (as shown in fig 2) similarly if we make ‘p’ cuts in one plane then we will get ‘p + 1’

pieces as shown in Fig 3.

Fig. 1 Fig. 2 Fig. 3
Fig 1 Fig 2 Fig 3
nd
• If we make a cut in 2 plane then we divide the cube in 2(p + 1) parts (as shown in fig 4) , if we make 2 cuts in

nd
same plane then we will get (2 + 1) (p + 1) pieces (as shown in fig 5) similarly if we make ‘q’ cuts in 2 plane then
we will get ‘(p + 1) (q + 1) ’ pieces as shown in Fig 6.

Fig. 4 Fig. 5 Fig. 6