wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Direction: A cube is painted and then divided cut into 336 smaller but identical pieces by making the minimum number of cuts possible. All cuts are parallel to some face.

How many smaller pieces have no face painted?

A
144
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
124
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
120
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
108
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C 120
Number of identical pieces 336=8×7×6. Hence we need 7 cut's in Z-direction, 6 cuts in Y- direction, 5-cuts in X-direction.



Means our cube cut into 8 parts along Z-directions say
nZ=8, Similarly nY=7,nX=6.

For total number of identical pieces we can say

nX×nY×nZ=336

{(nX2)+2}×{(nY2)+2}×{(nZ2)+2}

Now look at table below:
No. of pieces Formula Answers for
6×7×8 cube
3-face painted
(Corner pieces)
23 8
2-face painted
piece
4[(nx2)+(ny2)+(nz2)] 4[(82)+(72)+(62)]=60
Only one face
painted pieces
2[(nx2)(ny2)+(ny2)(nz2)+(nz2)(nx2)] 2[(82)(72)+(72)(62)+(82)×(62)]
Pieces no face
Painted
(nx2)(ny2)(nz2) (82)(72)(62)=120


(82)(72)(62)=120

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Summation by Sigma Method
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon